Boot Cycle problems on iPhone after overheating

Device: iPhone 6s

Problem: Boot Cycles and unnormal behaviour after some events of overheating

What happened: On one day my phone gets too hot in the sun three times (while navigating in a car). It showed the screen, not letting me do anything, I take it out of the sun and it cools down and lets me use it again. I get out of the car and into the supermarket, taking my phone with me. After 15 minutes I try to use my phone and notice that it is powered off – I was unable to activate it again via power button (battery was full when leaving the car). Back to the car, I plug it into the charger. It acts normally for 10 minutes, then starts to boot cycle (white screen with apple logo, turning black, white screen again and so on). I take it out after a few minutes. Once arriving in a hotel, I use the big iPad wallplug and my lightning cable and charge the phone with that. It turns on again and acts normally for about 10-15 minutes, then starts to boot cycle again. I tried to restore the phone, desperately hoping for a (very unlikely) software issue. Was unable to restore the phone because boot cycle always started before iTunes even got close to start the process on the phone. That produced the iTunes error No 2006. I started a one week hike without the phone at this point. Coming back, I plug the phone into my laptop again with lightning cable. This time, I am able to restore it properly. Counting the time for the restore process and the time afterwards, the phone behaved normally for about one hour – still plugged into the lightning cable, it then starts to boot cycle again.

More Context:

- Battery was changed from a 3rd party about one year ago.

- Power button started to work unregularly three weeks before the day my phone stopped working as described above. Had it repaired by a 3rd party two and a half weeks before that day. Camera did not work after the repair (so they seem to not have done a good job at repairing), I brought it back, they fixed it.

- Battery had first outage (meaning the phone suddenly turned of despite sitting on 25% battery) two weeks before the day described above.

- I had an incident with water with that phone in last december (= seven month ago). The side with AUX and lightning was not in the water; the other end was (about 2cm deep, standing upwards). Phone worked normally through all that, after some days about 1 square milimeter of the display had a discoloration (upper left corner).

Question: What is going on? Is there a serious way to tell what to do? Change battery? Or is it the mainboard? What would you do? Is it worth to even try anything?