Hello @Sandwich and welcome to the forum!
I'm sorry to hear about the trouble you are having with your phone.
Do you know if your phone still shuts down after a few hours if you disable the hotspot? Does it only shut down while you are charging your device? If so, could you check if you experience the same behaviour if you reboot your phone to safe mode?
If you answered yes to my last question I would recommend that you perform a software repair using Xperia Companion. Note that this will reset your phone in the process, make sure that you first create a backup. My suggestion is that you use the backup feature found on the main menu in Xperia Companion.
After you've performed the repair, try checking if you still experience this before restoring a backup or reinstalling any apps.
Let me know how it goes!
