Have you made sure theres no blockage in the new heatercore? is the coolant flowing when the thermo opens up? if the hot water isn't making it to the core the air isn't gonna be warm.
Damon, you must not know chevys too well. Ive put a heater core in every chevy I have ever owned. They always leak in the floorboard. Dustin, are you sure you have all the vaccum hoses hooked back up? Vaccum is what the makes the actuator move the blend door when you turn the selector. Since you have everything apart, can you see the heater core? If so, can you physically touch it to see if its hot?