Older Than Dirt

A while back I bought a xenon headlight conversion from prostreetlighting. Everthing works fine except when I switch to hibeam within a couple of minutes the thermal cb opens and my lights go out. Switching back to low beam restores the circuit. Here's my idea to correct this.... Install a relay just for the hibeams. Run a new thermal fuse link wire from the alternator or starter to one side of the relay contact. Clip the green (high beam wire) and wire the end going to the headlights to the other side of the relay contact. This would be my new hi beam circuit. The other end of the green wire (coming from the dimmer switch, hi beam wire) will terminate to one side of the relay coil. The other side of the coil will terminate to ground. Won't this work? Thanks....