It's not supposed to come on with the key. It ONLY comes on when the bike overheats.
I would suggest you take another look. Temp light should not come on.all three of my lights come on when I first turn the key on.
You're just wasting your time. The temp light ONLY comes on when it over heats.I really believe that like you bike does all 3 should come on when key is first turned on before starting, as a way to make sure warning lights are working. I am going to do more checking.