Efficiency is not just defined by more MPG.

A more efficient engine can also make more HP per gallon.

Gasoline needs to be in vapor form to burn and heat helps it vaporize.

I doubt you'll notice any gain in HP jut by changing the thermostat as others have said, it's in the tune.

Modern engines make a lot more hp per cube than older ones and the run a lot hotter doing it.

The reason cooler air into the carb makes more power is that cooler air is more dense so you get more oxygen per cubic foot. Again, you'll note that modern vehicles all use some sort of cold air setup. Back in the day when the carb got it's air from underhood it made a difference to lower the engine's running temps because the hotter the engine ran the hotter the air under the hood. Today, that's very old school thinking.