No fast idle when cold

I don't know what the heat has to do with the idle speed but the idle is controlled by the computer and will maintain whatever idle speed it calculates as necessary.
As for your heat, verify the engine temp first as you may need a thermostat. If you verify at least 195 degrees, then with the engine at full operating temp, locate the 2 heater hoses where they go into the firewall and feel them to see if they are both hot to the touch.
If you find that they are both too hot to hold, then the heat in that vehicle is controlled by a blend door that regulates heated air flow. It is operated by an electric motor/actuator. The problem can be that the actuator is stripped or inoperative or the door itself could be damaged. This is what needs to be determined by examining the actuator and see if it is responding to heat change commands or not.