Cooling system

Moin Moin, bought me a Yamaha 125ger YP, year 1998, is already an older gentleman but still quite well in the juice, since it is my first scooter, I am not so familiar with the matter yet and already the first problem is good. When I drove co. so 30 km today my temperature indicator went far into the red field and then waved up and down on the further drive, but mostly remained near the red field. The cooling water level is however fine. Maybe can someone might tell me what it might be because I still have little experience with the scooter. I have now removed the thermostat, but the display moves further just before the red field unfortunately I also do not know where it should stand at operating temperature. Greeting to all Ronni126