There is also the issue of the radiator - is it plugged?
There are several "checks" you can do.
Per
@scotman - turning on your AC should turn on the Radiator FAN and also the Blower motor.
Turn off AC - turn on HEAT - does it blow hot air thru the vents?
When you're at idle - do you get heat or AC - or is it weak?
Then when you drive does it get hotter or cooler depending on the setting?
IF it does vary, then that means the water pump is shot it is not able to move enough coolant to keep the engine cool, can't push out the hot fluid to get to the radiator.- needs RPM to push the fluid thru the motor to even get heat out of it, then to the outside - and if the pumps impeller is worn, only speed and RPM push the fluid and that's too much of the wrong thing to help with your situation.
You said the thermostat was stuck shut, so that creates a backpressure and the heater core can only do so much - that may mean the water pump has, or is, failing.