2005 Pontiac Grand Prix Heat Not Getting Very Hot

Hello and happy New Year.

First of all, we need to verify that the thermostat is the problem without removing it from where it is.
Start the engine.
Identify the upper radiator hose and the lower one.
We are interested in the upper one that is from the radiator upper side to the engine.
With the car running hold onto the hose. if you feel coolant running right away from the engine to the radiator, the thermostat might be stuck open.

Here is what you will need to do:

Disconnect the negative battery cable.

Partially drain the cooling system into a suitable container, to a level below the thermostat.

It is usually possible to leave the radiator hose attached and simply remove the thermostat housing (also called a water outlet) and flex the radiator hose enough to service the thermostat. It is good practice, however, to remove the radiator hose so the thermostat housing can be given a thorough cleaning. Debris on the thermostat housing sealing surface can cause leaks.

Unfasten the thermostat housing bolts and remove the housing.

Remove the thermostat by simply pulling out. Discard the gasket.

Hello JCWarrior_
disconnecting the battery is just to be on the safe side.
This will prevent accidental damage to onboard electronics or wiring if you accidentally cross up the wrong wires or short out a live circuit or bump on something.
Now, you said that 2 hoses running into the firewall and one was hot and the other was cold. Those hoses lead to the heater core. Note the one "hose"that is hot. When engine cool down, disconnect that one and using pressure water to the disconnected hose to flush the heater core.
I believe there is a blockage inside.