Phone overheating, will new battery fix it?

My Droid has become practically unusable, as the phone is overheating all the time and then it blocks and all functionality shuts down. Also, the battery has a short life and the phone shuts off from time to time by itself. I have offered it for repair in Europe, but the French repair center send it back, saying it was not repairable. I'm not getting a lot of service on this phone in Europe, as it is officially not sold here. I'm trying to find out if I can take any steps my self, like replacing the battery with the posted tutorial on this site. Will that likely help me? Or is it better for me to save the trouble and just accept that I waisted 400 EUR and buy a new phone?