Temperature problem / Punto

Hello together, since I have good experiences with forums about other cars, I have registered here now. My boys drive a Punto (hence the nickname) and if what does not run they naturally come to me. It is a Punto 55 6-speed (model 176), Built 7/96. Now to the problem: The water temperature indicator went down to the red area. First diagnosis was that the cooler fan was not switched on. I was the first to renew the temperature switch. Then went, but jumped the fan m.E. late (at first at 3/4). Then it did not work again. A wobble on the cable let it jump on. So – cable set Temp switch / juice/ventilator renews (40 € costs the thing). But still did not bring the solution. The water pump it is not, the hoses to/from the cooler are both hot, there is passage. You can also drive without further 25 km, until it comes close to the red area. I already bridged the fan switch, so that it ran continuously, nevertheless It goes off towards red. Since the display is relatively fluctuating, I have now suspected that the dealer is spinning for the display. Above all, because it has just been shown full red, the cooling water was far from overheating. Has any of you ever had this prblem? How much does the dealer cost? Are there other tips? In the hope of many answers many greetings Klaus