Start simple first. Remove the top plastic half of the steering handle, and check the connection to the temp sensor. The connector is located by the left brake handle.
Disconnect the sensor and clean the connections with some electrical contact cleaner. Reconnect and see if anything changes. IF you have the "green death" on the connector, it may have corroded far enough to prevent a good solid connection.
The temp sensor is located in the bottom plastic half of the steering handle. FWIW, the sensor itself rarely goes bad.
I've worked on enough Italian cars, and these bikes are no exception, to be smart enough to cover every exposed connection with some battery terminal spray (the red stuff like CRC 3175) to keep water, dirt, and muck out. See link below
https://www.amazon.com/CRC-Battery-Terminal-Protector-Aerosol/dp/B0013J7RAI