You are wrong. Don't know how convection currents would have anything to do with the fan, maybe have something to do with the pump or t-stat.
The fan depends on the coolant temp or the AC compressor. BTW, the compressor is turned on in defrost and recirc.
If it isn't overheating just relax, the engine can handle hot. There are millions of cars in Texas that don't need cooling help from humans.
If I were to think about something like this I would put a diode in the circuit.

 

Convertion currents happen when a fluid or gas moves over a hotter surface and pick up some of the heat for dissipation during the movement. This is how fans cool, by moving air. Old Volkswagens are great examples of air cooling.
Heat is the biggest enemy of engines and transmissions, I have already made a post about installing a transmission cooler.
I don't see the problem is taking control of an engine's operating temperature under extreme ambient conditions. Just a preference.

 

My previous HHR lost a fan blade and the car vibrated noticably. It was only a few mintes later that the fan self-destructed and lost all the blades. I was able to make it home without overheating. If you lose a blade you will know the next time the fan turns on, fortunately the fan is easy to replace.

 

Your physics lesson is a bit wrong too. Convection does not cool, it is a result of entropy, a systems tendency to move from order (cold) to disorder (hot).
Convection currents are when the warmer fluid rises and the cooler sinks, entropy (gasses are fluids). The fan cools by radiant heat transfer/diffusion, air moves over a radiator transferring heat to the cooler air. Actually, heating the cooler air not cooling the waymer
If there was no water pump the coolant in the engine would try to circulate in a convection current, Cooling would still occur from radiating the heat to the cooler air.
Old fashioned cars had a thermostatically clutched fan that would decouple when the air was passing over the blades faster than the fan was impelling it. That was to save the energy/HorsePower the fan absorbed. That might be what you are thinking about, electric fans don't use engine power. That was air passing over the radiator not over the engine, like air cooled VW, that is also radiant transfer from the fins on the cylinders and oil cooler.

 

Desertrat, you've given me an idea of where to look for a short in wiring of my radiator fan (the dark green wire or equivalent for my 2.4). I have had this on my to-do list for a couple years now ... Anyway, in my experience, my radiator fan turns on the second I turn the key, and stays on for about five minutes after taking the key out. So I'm guessing it's either a problem with the fan module, or a short (maybe in the dark green wire). I already checked the fuse and relay, and finally just removed the relay since it's not too hot in Minnesota. Did you end up installing what you were talking about?

With regards to the physics on heat exchange, from what I can tell and looked up, the radiator transfers heat out of the system through conduction, convection/forced convection (from the fan), and radiation.
I'm still trying to understand thermodynamics concepts of entropy and enthalpy, here's a decent youtube video I just found:

Good stuff guys, thanks.

 

Good point. But if we want to be professors, convection is due to differences in density, not temperature.

Density is usually inversely proportional ish to temperature. One exception is that rare substance we call water. As it cools and approaches freezing, It ceases to become more dense and actually begins to expand before it freezes. This leads to an interesting effect as bodies of water like ponds and lakes freeze. Convection prevents freezing by sending cold water down and warm water up... until it doesn't.

There are other exceptions.

 

I do know that the radiation of heat is from the air passing thru the radiator by the force of forward motion of the car or the fan pushing or pulling air thru the radiator core. A 2 row radiator is less efficient than a 4 row radiator. Apiece of tape on the grille will block air from entering thru the radiator and raise the temperature of the cooling liquid and effect aero dynamics of down force. I learned a lot in 35 years of experience with race cars.
weight control is speed and handling control . Then again protecting the radiator from damage, like in a baja style off road truck is also incredibly important.

 

The fan should run after shutdown IF the temp the ECM sees is above about 230F,
The fan runs when the AC compressor is running, it runs when in recirc and defrost modes with no AC light (you would not know unless you looked).
The fan runs when the ECM sees a temp above about 217F and turn off when it sees about 179F.

 

Back to the proposed switch, if you forget to turn it off, it will run the fan until the battery’s dead. Better to add a relay with the coil fused to someplace hot in run only, so that it no longer activates the fan relay once the ignition is turned off.

Disclaimer - Concept only. i’m not an electrical engineer. I have no idea if the fuses really needed or what its rating should be.

 

My theory is don’t mess with it! After 15 years of seeing all the electrical issues members have had. Leave it alone!