What did the mechanic do wrong if air conditioner in your 1998 Expedition only blows hot after heater core was replaced?

The mechanic most likely did not properly charge the A/C system with refrigerant after replacing the heater core. When a/c system is opened, refrigerant is lost which is why it is crucial that the system is recharged after any work has been done. Without the proper amount of refrigerant, the a/c will not be able to cool the air and will only blow hot air. To fix this issue, the mechanic will need to recharge the a/c system with the proper amount of refrigerant.