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Based on your description you have a partially stuck heater control valve. This is the only component that controls the heat. There is no temp actuator. Locate the valve and disconnect it to see if the heat starts to work. If it does then it is an electrical problem with the control module or wiring. If it stays cold then it is usually a mechanical problem with the valve.
UPDATE: Thanks to your help, was able to replace the DCCV today. Unfortunately, still no heat. The old one was stuck in the shut position, so I thought we were going to be good with the new one.
One thing that may help: I removed the #1 fuse to see if that made a difference. It did not. However, I did notice that when I removed the fuse, I could clearly hear the heater valve either open or close. Then, when replacing the fuse, I could hear it again.
It doesn't make sense to me. All three of those lines coming out of the DCCV are HOT. The heater core is not clogged. Could a bad climate control module be the culprit? Everything else works fine, just can't get any hot air.
Go back to the valve and the heater core. If you look on the heater core side the larger diameter hose is the top outer which is the return. The driver side is the top inner and the passenger side is the bottom. We should also make sure there is no air trapped in the system. There is a bleeder screw located in the rubber hose hooked to the coolant tank.