Cheers people, it's good to see so many people trying to bring solutions...
Paul: haven't read your U2U yet, will do as soon as I finish that message
Chass: Could you ask your sponsor for a price all included? (cooler + lines) knowing I will get rid of the heating kit...
Alan: guess what, I'm not even sure I will fit the shiny belt covers, now I'm worried gravels or stuff like this could go into the belts...
Soon for sale I guess...
Lucie: ... ... ... ... no way
Phil: now that's an idea. I will try using the switch from my road bike. But then I really don't think it's a switch problem, as it always gets on at the same moment, when the engine is very hot (after a race) and I'm slowly going back to the pits (so the engine is not really revving).