The wire on the temperature gauge of my Aprilia Leonardo finally broke near the socket so the temperature reading stayed on low/no reading. If you look you can see a metal pin on the gauge that the needle sits against. After about 2 minutes of motor operation the needle should move off that pin. If it doesn’t then check that wire.
To do this ideally remove the right-hand side inspection panel and the temperature sensor is towards the middle bolted into the engine block around the same level as the starter motor (the oil pressure sensor is much lower).
This can both come loose (mine did a year before) or finally snap off at the plug. The temperature sensor has a spade plug end on it so nothing special but you don’t have any slack to play with on the wiring loom so you need an extension wire but I discovered a nice fix that will probably work for you too.
Many months ago I had picked up a junk microwave from the road side: I had pulled it apart to see what was inside and I remember keeping all the wiring looms from the microwave. The wiring loom connects all the microwave door interlock switches together to the control board. Looking around for suitable wire to repair the bike I noticed that the microwave loom had these nice sockets with moulded plastic covers and reasonably good sized cable. The cable lengths are only a short distance of a few inches/centimetres but that’s all I needed.
I tried one of the sockets fitted the temperature sensor on the bike and it clicked on perfectly. So I chopped off one of the sockets with about 3 inches/8 cm of wire on it, stripped back the end and then stripped back the end of the broken wire on the bike, cleaned the corrosion away and then used a barrel/coupler connector to join the new bit of ex-microwave wire to the bike wiring loom wire.