So what did you end up doing Madakor? I am having the same problem but my phone wont even stay on for more than 5 minutes while connected a charger. I am pretty sure it is the phone itself that is damaged, not the battery. I also have no sound coming from the speakers: ringtone, music, etc. This is all a result from the phone being dropped in water. After drying it out and cleaning it out completely it started to work fine except no speaker sound and no longer being able to charge the battery. The "temperature too hot/cold" message started to appear more frequently.
I am trying to repair this myself with replacement parts, any and all advice would be helpful.
Thanks!