Stop in for a cup of coffee

Nope. See, what the thermostat does, is to keep the coolant in the radiator till it cools off, By the fan and air flow. Without the thermostat, the coolant does not stay long enough in the radiator to cool off.... eventually it will over heat.....or not.....
Most likely engine will never reach operating temp. If it boiling hot out and your pushing the car, then yep stat is best left in.