Heater cores are the #1 problem with the 82-93 mustangs. On my 1982 GT I replace the core 3 times. Its a royal pain in the a$$ to change. Basically you have to removed the console, drop the steering and dash and break open the AC to remove the box containg the heater and evaporator core The last time I just bypassed and went without heat. Here in Texas
that not too bad. There's a couple of ways to check. Remove the heater hoses and bypass (loop together) the hose. If it stops then its the heater core. Also, if it has a glycol odor then its the heater core. Good luck.