Heater core

I've been told my heater core needs replaced, but there were not diagnostic tests done (at least not computer/machine based). Here is what is happening:
* When outside temp drops to 30s or below, cab does not get warm and blower becomes very insufficient.
* If it's in the 40s or above, hot air comes out, but does not blow hard out of vents or defrost. A/C works perfectly and blower runs at full capacity.
* We don't go through any coolant, do not smell coolant, and do not have the fine mist of coolant in the cab.

Thanks for any help, and please let me know if I can clarrify.