The heat in my 98 subaru GT is blowing cold air.

Did you turn the temp switch back to the blue (or cold) end? If it's still in the red section, if will only blow heat.

I assume you don't mean it just blows cold until the engine warms up. Could be sticking thermostat, air in system, low coolant, vacuum leak affecting flapper door.

Make sure coolant (Water Is full)
The system is clog. Or Heater valve is not open when you slide the control knob to hot or cold.
-Check the heater valve by moving the control knob to hot and cold. The valve turns or not. If it turns then the system is clog. If not turn at all then the valve is not function. (the cable might be slip off/Hook or connect it back to the valve)
*If it turn then the system is clog.>>>Need to flush.
-Disconnect the heater hoses from engine (Both hoses) and flush it with garden water hose from both direction for couple minute.
Reconnect, fill or add more water to radiator to full then run.
You should be good to go.

Mai Lor

maybe heat control switch which opens a valve lets hot water into heater core
or thermostat faulty

The air is mixed and routed inside the dash by some flaps. In your case the flap that regulates the mixing of hot and cold air for the passenger side is broken or stuck in the cold position.
The only way to fix that is to remove the dash , access the air system and fix the flap.

have the head gaskets checked. a shop can do a test for combustion gases in the cooling system. if gases are present, the heads need to come off.

try changing the thermostat for starters.

Heater core..easy to replace..find the complete tear down and rebuild book for your car at any part store and follow the directions on how to change it.

Radiator... if its the rad then you pretty much are looking at about 800.00 to 1100.00 for this .
If its the radiator... you will notice your car will start to over heat.
It could be even more serious..like the block might be cracked.
If you see like a steam that looks like smoke coming from the tail pipe then its the block.
Again can be fixed for about 12 to 13 hundred bucks.
Hears hoping im wrong on all accounts.
cheers

heater core could be plugged,try removing both heater hoses to core and back flush

Have you checked the heater core or maybe a door not engaging also check your vaccum lines.