The cooling systems in the 308/Mondial are barely adequate--they are "just enough" to get the job done when they are in good working order, and unlike a modern car, they don't have much extra capacity in "reserve." So a partially clogged radiator, marginal thermostat, improperly bled system or leaking expansion tank cap, etc. can cause the car to overheat or at least run too warm.
The most common things that seem to go wrong are:
1. Fans not coming on
Cause: usually the fuseblocks. Sometimes the thermostatic switch in the radiator. Easy to check. Just pull the two leads off the thermostatic switch at the bottom corner of the back side of the radiator. Use a connector or a wire with alligator clips to connect these two leads together. Turn on the ignition switch (car can be stone cold). BOTH fans should come on. If they don't, the issue is probably the fuseblock. Could also be a fuse, a relay or least likely, a fan motor. Each fan has its own fuse and relay. The left fan is also activated by the A/C so it has a second relay. If they come on when you connect the leads, but not when the car is hot, the switch in the radiator is bad. This can be replaced with an expensive part in a yellow horsie box from Ferrari, or even better you can get a 180° switch (slightly cooler and way better) from David Feinberg at Ferrari Service of Bedford in NH as part of his "Temperature kit" which I highly recommend.
2. System not bled completely
Bleeding the air out of a 308 is a little bit of a pain. Not hard, just takes a while to do it right and it really is necesary to get it right. If there is too much air in the system, it expands too much when the car gets hot and forces too much coolant into the expansion tank. It overflows. Then when it cools, the car has less coolant and more air. Then the next time it is warmed up, the situation is a little worse. It just gets worse and worse. Instructions to bleed are here. I actually bleed the air out of my radiator now and then as a matter of course. When the car is hot, even if shut off, the system is pressurized. So, pull it in the garage, shut it off, pop the front lid, grab a paper towel, open the front bleeder screw and let the air out, catching the coolant drips with the towel. Now close it up. Takes about 30 seconds and you will be shocked that you can get a bit of air out of the system virtually anytime you do it. If you put a neoprene washer or rubber o-ring from the hardware store on the bleed screw, it can be finger tight and won't leak or break, as those fragile brass screws are known to do.
If you keep bleeding the system and continue to get a lot of air out of it every time you drive, and the car runs hot, you may be getting air into the system someplace, such as a bad head gasket or even a loose hose clamp. I have heard of cars that needed to have the head bolts torqued to repair this issue.
3. Bad expansion tank cap (i.e. "radiator cap")
This one is common. A very cheap part and you wouldn't believe how often these fail. Mostly just because the gasket gets old and "smushed" so that the cap starts to leak before the system gets to pressure. If this happens, the water can boil at a lower temp. Result: the car overheats. Get a new one cheap....and it's even the right one for your car...from Ricambi here or from Ferrari Service of Bedford. See additional discussion below on the operation of the radiator cap--be sure you are not blaming the cap for a system that is not properly filled and bled.
4. Clogged radiator
It happened to me a couple years ago in my Mondial when deteriorating rubber hoses clogged the radiator with small rubber particles. I had mine re-cored for about $350 and then I had essentially a brand-new radiator. More often in older cars is a radiator which is partially clogged due to corrosion in the system and sometimes a radiator can be repaired by a radiator shop by "rodding" it. (They take the top off the radiator by unsoldering it, then run a thin metal rod down each cooling tube to scrape out the gunk.) However, some shops will not rod an old 308 radiator because they are afraid the metal is too thin and fragile, and they don't want to be responsible for screwing up a Ferrari radiator. I chose to re-core mine as a result. Drain the cooling system, pull the hose off the top of the radiator and look in there with a flashlight. You can see the top of the tubes and get a good idea what is going on. Re-coring means that they replace the cooling section in the middle of the radiator with brand new metal, but re-use the top and bottom of your exisiting radiator with all the mounting brackets, etc. It's much cheaper than buying a new radiator, and the modern cores are more efficient than older ones anyway because of a better design. There is absolutely nothing wrong with re-coring a radiator as long as the shop that does it knows what they are doing.
A bad thermostat that doesn't open enough or at the right temperature will not allow enough coolant to reach the radiator...and that is bad. Even if your radiator gets hot, you could still have a thermostat that is not opening fully. I also had a thermostat fail once where it opened too soon, and the car couldn't get warm in cool weather. It seems like thermostats these days are junk, and they are definitely one thing to check carefully.
An old trick with some cars that run hot is to remove the thermostat entirely to increase flow to the radiator. It won't work on a 308/Mondial because it uses a special kind of "dual throw" thermostat which directs coolant in one direction when closed and another direction when open. Hence, without any thermostat at all, the coolant is not directed properly to the radiator. (Some will get there, but not enough). Removing the thermostat from a 308 definitely will not help keep it cool!!
For any car that is running hot, I would simply work my way down this list. Start with a new expansion tank cap (cheap insurance and takes 2 seconds to install), then add some coolant, bleed it correctly, check the fan operation and take it from there. Since the thermostat is the most work to replace, it's the last thing to replace if nothing else works. Check out my complete thermostat tutorial!
My Recommendation for all 308s: 180° THERMOSTATIC SWITCH
When you are driving along on the highway, even on a hot day, lots of air is blowing through the radiator, so the coolant flowing from the radiator back to the engine is much cooler than the engine itself. In that case, the thermostat is in complete control of the temperature of the engine. It adjusts the coolant flow to keep the engine at its set point because the coolant coming back from the radiator is well below the engine temperature. It has an easy job to simply let just enough coolant through to keep itself in its happy place.
However, when you are in traffic, the fans have to push air through the radiator, and to do that, they have to actually come on! They are controlled by the thermostatic switch in the radiator. The stock thermostatic switch comes on at 195° F (92° C). Keep in mind that the radiator is always at least a little cooler than the engine because the coolant has to run all the way up front through pipes, and it cools a bit on the way. Furthermore, the switch is on the bottom right of the radiator, while the hot coolant comes in on the top left. For the coolant in the bottom of the radiator to get to 195° to flip the switch, the engine is probably at 210° F or higher. In that case, the thermostat is open all the way, trying like crazy to keep the engine cool. It's doing all it can do, but the water coming back from the radiator is not as cool as it needs to be to get the job done. So in traffic, the thermostat is not in control of the engine temperature. The thermostatic switch on the radiator is the thing controlling your car's engine temperature, not the thermostat. Swapping the 195° thermostatic switch in the radiator with a cooler 180° switch will get those fans moving well before the engine goes over 200° so your fans are doing their job a little sooner and your gauge should sit in the middle just as it does when you are on the highway. Why? Because you are essentially now handing the job of controlling the engine temperature back to the thermostat, where it belongs. No matter what thermostat temperature you decide to use, everyone should be using a 180° thermostatic switch in their radiator. Let me reiterate this for emphasis: if you don't have a 180° thermostatic switch in your 308 radiator, you should!!! Every 308 should have this simple modification! Ferrari goofed on this. The thermostatic switch on the radiator of any car should be a little lower in temperature than where you want the engine temperature. That's car cooling system design 101. That's the reason a modern car, once warmed up, always has a consistent engine temperature even on a hot day sitting in traffic. You will be amazed what a difference it makes in traffic/stop&go driving in your 308. You can trust me on this, I'm not trying to sell you anything. I don't sell the switches. Get a 180° "Temperature Kit" from David at Ferrari Service of Bedford. Very cheap and easy to install (although you do have to dump your coolant to do it). It comes with the right thermostatic switch, thermostat, gaskets, etc.
What does the radiator cap (expansion tank cap) actually do?
The reason the upper fill level line is well below the top of the expantsion tank is to leave an air space inside the expansion tank into which the coolant will expand as the engine gets hot. The volume of that expansion space is not random. As the coolant expands into that space, it compresses the air in that space, creating a pressurized system. This pressure is extremely important, because when you put the coolant under pressure, its boiling point goes up. The engine creates temperatures well in excess of those required to boil water. If the coolant were to get hot enough to boil, the cooling system would find itself under extreme pressure from steam creation, it would be full of water vapor bubbles, not cool efficiently, and your car would overheat. The job of a radiator cap (technically the "expansion tank cap" in a 308) is to hold the pressure in until it reaches a certain level, then relieve any pressure beyond that. That prevents the pressure from getting so high that you burst a hose. Typical Ferrari caps are 0.9 or 1.1 bar (13 and 16 psi respectively). The stock radiator cap for a 308 is 0.9 bar but if your hoses are in good shape, there is no harm in a slightly higher working pressure using a 1.1 bar cap, which can better prevent boiling in a very hot engine.
If you overfill your coolant, there is not enough space for expansion. The result is a system working pressure that is too high--and the cap relieves the pressure and your car spills coolant on the ground. If there is too little coolant (and sometimes this is because there is a giant air bubble in the radiator that hasn't been properly bled, even though the level in the expansion tank looks fine), the result will be too much air in the system which means the pressure will (initially) run too low. Yes, that's a problem too because what happens is that the coolant will start to boil in the engine, leading to water vapor in the system, which then spikes the pressure up and...you guessed it....makes the radiator cap do its job and release pressure by spewing coolant out. Two different problems, same result.
Many times, what appears to be a bad radiator cap is just that. But other times, it is indication of a cooling system that is not filled to the right level or properly bled.