Keeping important apps alive even on overheat
I don't know if this will work in your situation (and I can't test it myself) as in your situation it seems the killing of processes is done for safety reasons and not just to free up memory but it could be worth a try.

The app is called MinFreeManager (requires root) and there is a good guide here. Taken from the link to the guide, here is an overview of what the app will do;

ActivityManagerService.java looks at the 'importance' of running processes; foreground apps, services, content providers etc, and prioritises them for close order in an oom (out of memory) situation. Each process is assigned an oom_adj value. The lower the value, the less likely Android is to close the app when it starts to run out of memory.

These values are managed by Android at runtime so a processes oom value can and will change as it changes state, from foreground, to background to idle etc.

The app can adjust a processes oom_adj values to your own custom values so you can try and manipulate which apps Android will close first and at what stage of low memory on the device.

Like I said, this is just a very basic overview. Follow the link to the guide and you will find all the information you need to give it a go (Could go on for pages if I tried to explain in full detail).