I just would like to correct myself. I said that is doubtful that it is the heat core but to check the temp door. Well the door that controls the tempature is inside the heater core. Don't know what I was thinking.

 

Like others, I would also advise to check your coolant level and the condition of the coolant. Also if you have had anything done to the cooling system recently (flush, coolant hoses, thermostat,etc.) was the system properly bled. I would also have to say from my experience that when I've seen heater cores go bad 9 outa 10 leak into the car. Once again try everything else first because they are a PITA!!

 

I was actually talking to a 95 Accent owner last week who had a similar problem... he said it was an air pocket in a cooling passage. He had just swapped in a new motor (1.5, not a Beta, sadly *lol*) and some air had gotten into the system. He got it flushed and he said after that the heat worked fine. BTW he's from my town, up here in frigid Canada.