no doesn't need a thermostat for loss of coolant- hook it up to a pressure tester and pump it up to the caps rating- if the pressure drops off, you definitely have a leak, but look for one anyways while its pressurized check everything including the radiator areas and any lines or hoses to and from the radiator, and the heater core hoses even check the floor board of the car in case the heater core is leaking, if you find absolutely nothing, i would start to worry if you might have a leak internal to the engine.
