This air hose reel was broken several year ago. Knowing that it could be dangerous to work on such a machine I put a hold until I could be confident that I can try to repair it. The day has come and I finally open the thing. There was no danger because the coil spring was no more attach to the main pivot.
So, I remove the strap that constrain the coil and let it free. At this point, there was no tension on it. I make a dummy holder, test the way I should manipulate the coil during the heating process. I place the end of the spring into the dummy, heated it to red and squeeze it to form it around the pin. The most tricky part is to put it back in the reel and turn the coil in order to be able to constrain it within the strap and have both ends fixed. Good luck if you need to repair one.