"Thermostats" are installed, in order to make sure that the engine is running at the optimum temperature, and consequently, optimum efficiency,- regulated by the car's cooling system. As for your observation that mileage is better on a car without a "thermostat", where the temperature gauge is only at "1/4", that is also my experience in my previous cars, which is on the contrary.

Some say that they're installed for countries where the weather is usually cold to bring up the engine temperature fast when you start the car.