I am have the same problem with my 06 Monte Carlo LT. Took to the dealer. Its a head gasket leak.
The dimmer switch, on your 2001 Chevrolet Monte Carlo, is located on the lower left hand portion of the dashboard. The dimmer switch is just below the heat vent.
Your heater core is likely bad
500-600 RPM 600-700 With AC or Heat on high.
you have a blown head gasket
Turn on heat, on high till car warms up.let it cool down that may do the job... Check fuild.
Coolant leaking onto the floor of the passengers side or out drain tube for a rupture no heat for a blockage.
inside of the door of the Monte Carlo there are two tan wires, a larger one, a smaller one, a blue wire, and a black, try to get some shrink rubber for wires or electrical tape either one, I prefer the rubber all you need to do is put it on one end before tieing the two wires each together and then take a lighter and heat the rubber and it will shrink around the exposed wires. When you put the door trim back on the locks will work I recently worked on a 1992 Monte Carlo with the exact problem.
If it's interior heat you are talking about, it could be the thermostat. If you find your temp gauge is fluctuating all over the place, change the thermostat. If not, it could be your heater core. You could try flushing it out.
Check coolant level? Heater core plugged restricted, or airbound? Defective thermostat? Water pump not circulating coolant? Heater control cable not adjusted properly?
There is a heat censor on the tranny and it is worn so now it takes longer to warm up.
Effectively all the fuel that it burns while idling. You are getting 0 miles per gallon while idling.
You need to adjust your idle.