heater core help?

What is your question?

bought a 94 civic in the summer time and was happy the a/c worked good, cold air not a problem during summer. now we're getting into fall and soon winter so recently i gave the heater a try. i cranked the heater up all the way and had it maxed out on the heat side and what i got was not heat, not even warm. i checked the coolant levels and it looks like its topped off and not low, i tried all the other functions on the panel like the windshield, the feet, and such, but still no luck, tho the back window defroster works. I took it to a relatives mechanic and he used a pressure type of method where he hooked something up to the radiator to blow out gunk and such to unclog the heater core. after he was done he tried the heater again and it didn't work, so he told me i would need to replace the heater core. I wanted to know if replacing the heater core would fix the problem? i don't know much about cars but i have been suspecting other car parts that may be the problem such as the thermostat. help please?