Mmm. Would it? When i took out my thermostat it fell apart. In bits!
The cooling system changed the way the bits must have moved back and forth.
Don't trust the clock on the dash, Have a feel about the hoses after a few runs and see if there is any change.
if a thermostat siezes closed then it would heat up quickly, if it fails in the open position then things would be cooler, and you would use more fuel.