2005 Pontiac Montana heater

Chances are you have a blend door that is not closing off the outside air when you turn on the heat.
If this system is the same as the ones I've worked on, the blend door actuator in question is the one on the drivers side, under the dash about half-way up.
Remove the actuator motor and close the blend door by hand, now with the heat on you shoudl only get heat. If this cures the problem, then you know that either the actuator isn't working or the blend door is failing to close completely.
You can see the actuator move when you turn the selector to heat and then to the other settings.

You have an air tempactutor so first thing is t o pull hvac fuse ofr 60 seconds with key on and theymay reset. Then check to see if one in first pic works. Secondpic is also for air temp see if the spring is broken or is the cable works properly. Ther may also be an actuator for right and left sides. One other thing make sure your coolant level Is full that is the number 1 cause of poor heat low coolant. If it is then have system pressure checked for head/intake gasket leak

If I understand your question correctly, you have heat in some modes and not others. This pretty much proves the blend door actuator is working and the system has some sort of programming issue that could even be intentional but possibly a problem with the control head.