A thermostat is designed to keep the engine running at a particular temperature (and are rated accordingly). Unless outside conditions are either hotter than the surface of the sun or colder than a witch's chesticle, then it will work perfectly fine regardless of the outside temperature. The RADIATOR on the other hand, is dependent on air temperature, and if it is insufficiently sized for the task then it may not be able to bring temperatures down far enough to keep the system in equilibrium, and that is when engines overheat. Still, I can't imagine having to change a radiator on an import to a bigger/thicker one unless you intend on doing some hardcore towing/track-work (which place much larger demands on the cooling circuit).