Hi, I am a professional certified mechanic, with an engineering background, and 35+ years experience. I will do my best to assist you today.
I am an electrical specialist, and I have dealt with a lot of problems like this before. The PCM, and the BCM are both involved with the AC system, but only the PCM deals with the temp sending unit, so if there was a module problem that could kill the function of these two systems, it makes sense the PCM would be bad. I see you have been down that road. There are a lot of possibility’s here, and this type of problem can get real deep real fast. What I have found so many times is a trouble code tells what the computer perceives to be malfunctioning, but doesn’t very often tell you why, or if the part is really acting up, just like the temp sensor, so normally I test the sensors before changing them. What I am suspecting is a possible bad connection at the PCM, or even more likely a power or ground failure to the PCM. A PCM will almost always have multiple power in and multiple ground wires. If it looses power or ground on any of it's power or ground wires it will loose partial function. Power or ground failure can be in the PCM connector, where the contacts come together, or where the connector crimps to the wire, these types of bad connections are hard to ID. I would get a complete pinout for the PCM, and verify all power and ground inputs. If you have any more questions I am here to help. Good luck with it, and Thanks for using Just Answer.
I hope this helps, 100% satisfaction is my goal. Myself personally, and Just Answer are here to serve you. If the answer is not clear, let me know what additional help you need, and I will assist you further. When you're satisfied, and feel you can leave a positive feedback please accept my answer. I don't get paid unless you do. A bonus and positive feedback are always appreciated, good luck and Thanks.