1995 Chevy Beretta overheat

Hi, coolant is up where it should be and temp goes up to about three quarters hot on the idiot guage and then drops down quickly to a little above a quarter if I let it sit and idle for about 15 minutes I dont see the fan kick on? The outside temp. Is in the 20's so I dont know if fan would kick on or not? Could it just be thermostat sticking? If the thermostat is not working properly would that have anything to do with the fan? Thank-you so much.