Heater blows warm air but not constantly

Is the cooling system full?

You did not say how long that takes or if you are starting with the engine already hot, so the best guess is the heater core is partially plugged. Does the temperature gauge reach normal temperature? If it does not, the thermostat is the best suspect. If it does, drive at highway speed long enough to get the engine hot, then stop and feel the upper radiator hose. It should be too hot to hold onto for very long. Next, feel the two heater hoses. If they are not as hot, have the heater core flushed first.