You don't want to remove the heater core. The heater box assembly is the first piece they put in the car when they assemble the interior. You have to remove the steering column then the dash to get to the heater.
Since you live in Phoenix you may not have a thermostat in your car. I grew up in L.A. and cooling systems get seriously abused where it doesn't freeze.

 

that would honestly makes sense..i use to take my tstats out of my older cars.this one im not sure what the previous owner had done..i think its a good idea to replace the tstat anyways thank you for the replies