The Mazda dealer replaced the PCV hose and now the heat doesn't work. When I called them to see if they may have done something to contribute to the heat not working, naturally they said no, and that I should check the thermostat. I need to know how to replace the thermostat.

Just the hose or the PCV (not pvc) valve? The hose is probably a dealer-only item - go to the Mazda parts department w/the broken piece and they'll get you a new one. The PCV is avl. @ most auto parts stores - and is cheap - <$20.

GL,
Td

U have a broken hose, replace the hose . Take the broken hose to a parts dealer. Refill the master cylinder that powers the hose,with the proper fluid. One end of the hose will screw into master cylinder.

No this wont cause an overheat problem. Check the coolant level , check to see if the fans come on after it heats up. when the car is warming up you can check the thermostat, by touching the top radiator hose, after a few minutes the hose should get hot, this indicates that the thermostat opened up and is working. If it doesn't replace the thermostat. If it doesn't over heat until you start driving , then suspect the water pump. The impellers can slip on the shaft and not have enough flow to keep it cool.

You just told us

PCV Hose

Take it to an auto parts store
or dealer if not at parts store.

Most PCV hose are formed and available from the dealer only.

check vacuum leaks special idle valve to the pcv valve

You have the wrong type hose on the pcv valvle. It isn't vacuum hose.

the part that you describe is the valve cover, yes they do leak oil, especially if the pcv system is not working properly

the pcv vaulve is a6.00 part at the parts store and only takes a few sec too install
someones treying too rip you off

The problem is a faulty solenoid in the vapor recovery system. The solenoid is sticking open and allowing fumes from expansion of fuel in the fuel tank to enter the air intake and smother the engine. This is how the Mazda service tech explained it to me. It is a known problem on the Mazda 3 in various trims which Mazda refuses to acknowledge. Usually the check engine light comes on and the engine diag code reads mass airflow sensor, which is incorrect. I dealt with this for 6 months on my wife's 2005 Mazda 3i before the dealership figured it out. My cousin bought a 2007 Mazda Speed 3 which developed the same problem after a few months and was cured by the same fix.