Cooling water temperature indicator failed, fan always runs….

Yesterday I had an unpleasant experience, which pointed to an electronic problem. But everything in turn: On the way home there was a lot of traffic to the column drive over the San Bernardinopass. Then I decided to take a break and steered a parking lot. At the stop I noticed that the fan of the engine cooling was running at the highest speed. I still let the engine run a little and then switched off, water temperature as always nice in the middle. When driving after about 20 minutes the fan ran again directly with the full speed. I also had to give gas so that the engine could start up. But because of the outside temperature of 28 degrees still looked like normal. Here of course with switched on climate. After a further 70 km drive and a stop of approx. 30 km. I had problems again during the further drive. Again the fan went to full speed, the engine still needed to jump again to the speed, then ran again with increased speed, although still cooled down. By repeatedly returning to the normal empty run. In addition, the cooled water temperature was still quiet.