I have a 2001 hayabusa the temperature guage isn't working where should I start

You need to find the engine temp sensor. It should be in the cooling system. Check your wiring diagram if you have one. Disconnect the wire from the temp sensor and turn the key to the on position. Now touch the wire to a good ground and note what happens to the gauge. If it goes all the way up or down the sensor needs to be changed. If nothing happens you need to check that the wire going from the sensor back to the gauge is good, you can disconnect the wire at the gauge and check by connecting both ends to an ohm meeter or use a test light. If this wire is goo now you need to check for power on the other side of the gauge. If no power that is the problem. If you have power the gauge is no good. That is it. I hope this helps.