The Evaporator and the heater core are two separate parts.
You could turn down the temp, then open the hood and see if the compressor clutch is engaged or not. If it's engaged, then the inner part of the compressor pulley will be turning.
If it is, then you could try adding refrigerant. Go to an auto parts store and get a kit to recharge the system. Some cans of refrigerant come with UV dye. If you buy a UV flashlight, you can use it to find the leak, that is if it's in a place you can see. Hook the can to the low pressure side and let the compressor suck it in. The air from the vents should get colder.
If you have a leak, as I do, you can repeat this process over and over gain. I couldn't find my leak, so I'm guessing it's my Evaporator.
Others here might be able to give you other suggestions. There's a lot of information on this forum regarding A/C repairs.