The idea that something is causing it to overheat indicates a short or excessive amperage being drawn. There are different modules for different things related to the HVAC. The interesting part is that nothing is causing a fuse to blow and protect the circuit. Was the original OEM part burnt the same way as the replacement? I'm asking only because you mentioned they were cheap replacements and sometimes they don't meet the same specs.
I just looked through the cluster schematics as well as the HVAC schematics and don't see how the two connect.
Here is what I would do. If you have access to a scanner that can check the can bus system, I would test the entire can system to see if there is anything that indicates a specific breakdown. CAN stands for computer area network. Here is a video showing how that is done:
If you are unable to do that, the next thing would be to disconnect each of the affected components and start plugging in one at a time to see which circuit is causing the problem. That is a more expensive way simply because you have to waste a module in testing.
Regardless, I am attaching wiring schematics for you. The first 4 pics are the instrument panel schematics. I had to cut them in half to make them readable, but I did overlap them so you can follow them.
Pics 5-8 are of the HVAC. I also overlapped them.
Take a look through them. Hopefully something will help. And yes, a shorted motor can cause an issue, but again, a fuse should protect the circuit.
Let me know.
Images (Click to make bigger)
Thursday, October 1st, 2020 AT 7:18 PM