Heater blowing warm air and gets cooler when I increase fan speed.

i would be looking at the temp of the inlet and outlets of the heater core. look at the temps of the rad as well. you may have a clogged radiator too. Roy

Sounds like you have a restricted heater core - If you feel the two hoses going into the firewall from the engine (5/8 and 3/4 inch hoses ) If this is the case one will feel cooler than the other. You can remove the hoses and try flush out the restriction with a gardebn hose alternating each input to the firewall. Check also your temp gauge, if its not reading around half scale you may need a thermostat. Good Luck