I had a space heater plugged into my hall bath outlet. It's not a GFCI, ALL other outlets in house work. I just changed out the outlet that stopped working and nothing changed.

By current code standards the bathroom receptacle should be on a 20 amp branch circuit that is GFCI protected.

1) I look for another bathroom with a GFCI protected receptacle and reset that receptacle.

2) I'd check the circuit breaker in the panelboard for this circuit and make sure it is in the "ON" position.

I would do this by switching the handle all the way to the "OFF" position and then back to the "ON" position.

3) Make sure that the circuit is a 20 amp circuit and not a 15 amp circuit.

4) Make sure that this heater is designed to draw less that 20 amps for proper operation.

Your gfci receptacle may be protected at the breaker box with a gfci c/b in the panel