Otto, a thermostat indeed regulates engine temperature, assuming that the radiator is big enough to provide the required cooling.
Just the name "thermostat" is made up of thermo or heat and stat or constant. The engine will heat up initially, with the thermostat closed, then will open to regulate at or near to the rated thermostat temperature. If the engine generates less heat (moderate speed on flat ground), the thermostat will close a bit, and if you mash the gas to climb a hill, the engine will generate more heat and thermostat will open to provide more cooling from the increased flow thru the radiator.
