OK, so normally I would just discount this absurdity out of hand. But being that this is from you,
@Steve83 and you have a history of being smarter than most...I am going to have to dig into this deeper.
The notion that the thermostat has no capability to regulate engine temp is an interesting theoretical hypothesis. If the hypothesis were true, then the theory can be proven. The thermostat being a capillary controlled mechanical device that opens an orifice to restrict flow thru the primary heat exchanger. So let's just stress test your theory.
I have a 82 Ford 351W heat engine. Let's assume that it is in it's as-designed configuration. Let's assume that it has a 185 degree thermostat. And for the purpose of destroying your hypothesis...let's assume it is installed in a Mastercraft Boat, floating in a Lake, with a reservoir temperature of 60F, and for the purpose of this analysis...let's assume that the lake is of infinite heat capacity. (Fans, radiators, convection coefficients, thermal transfer, delta T's all go away.) The Tc is established at 60F, with a thermal capacity of infinity. By your theory, the thermostat is not capable of regulating engine temperature. But if you remove the thermostat, the engine temperature will reach a steady state temperature of about 70F. And if you plug the thermostat orifice, the engine will reach an eventual steady state temperature of T(h). But we know that the engine temperature is modulated to reach 185 degrees, and the orifice size is proportionally adjusted to achieve that temperature. There is some hysteresis, and some transients, but fundamentally the coolant temperature is maintained at 185. Therefore the thermostat does control the engine coolant temperature, and therefore your hypothesis fails.
I'm not going to debate the fundamental inaccuracies of the Carnot Cycle efficiency thermodynamic model, except to say that is is also absurd, and like most complex engineering analysis...the solution is constrained to the assumptions. If you assume enough, you can reduce engine efficiency to the classic (Th-Tc) / Tc ratio. But everyone knows that Carnot was French, and the French have been stealing technology and fouling up the world for about 2 centuries. I urge you to visit the Musee des Art's and Metiers if you have the opportunity. It was enlightening for me, and brought home the concept of concurrent invention...but I digress.
I once explained to my Thermodynamics Professor that one cannot reduce an internal combustion engine efficiency to (Th-Tc)/Tc. Because if you do that, you cannot explain how a high performance engine can be more efficient than a low performance engine. They always both have identical Th and Tc. But they have vastly different heat conversion efficiency in both Specific Fuel consumption, and Horsepower per unit displacement. So you might as well "assume" that the answer is "SEVEN" and move on. Back in the 1980's, I actually made a list of my favorite "answers." Those answers include "superman" , "watermelon", "seven", "Napolean," and "his left foot." They are all awesome answers, taken from the back of trivial pursit cards. And they have just as much application to oversimplified engineerig analysis as any other answer.
Gotta run...