Yep its sounds like you have a blown head gasket this will fill the heater core with exhaust which causes the heater to stop working. Here is a guide that will help you confirm the problem
https://www.2carpros.com/articles/head-gasket-blown-test
This guide an help as well.
https://www.2carpros.com/articles/engine-overheating-or-running-hot
Water pumps can develop loose impellers, but that's more of a Volkswagen thing. Poor circulation will result in cool radiator hoses, but the gauge will read "hot". If the gauge reads low, what makes you think it's overheating? Look for bubbles in the overflow reservoir. If the coolant is cold, you know it's not overheating.
Do not remove the thermostat. In some cases, that will cause overheating because the coolant won't stay in the radiator long enough to cool. More commonly, the engine won't reach operating temperature. Parts won't fit right leading to rapid engine wear, and the fuel system will not go into "closed loop" and fuel mileage will go way down.
The pressure cap simply allows system temperature to go above 212 degrees without causing the water in the coolant to boil. It doesn't CAUSE the temperature to rise.
Please let us know what you find. We are interested to see what it is.
Cheers, caradiodoc
Wednesday, January 8th, 2020 AT 12:30 PM
(Merged)