My approach would be to start by removing the back to see if I could locate where and how the harness goes through. Shouldn’t need to disturb the innards. If it looks possible, I’d probably see if there is a YouTube of someone servicing an interior component. I love YouTube DIY videos.
Another approach might be to look at a schematic to see how the units own temperature sensors work. If they are 10k sensors, it’s pretty easy to sense that directly from the external PCB using an arduino or ESP.