I had not mentioned that before leaving Carriacou the engine did not start. There was no lighting on the instrument panel
It took a few minutes to find that the 12V + cable was corroded and separated from the panel. So, I removed the corroded part of the cable and the engine started. After less than a few minutes the sails were up and the engine turned it off for the next 50 hours while we sailed with the asymetric spy and the mizzen staysail on a great broad reach with 18 knots of breeze. The “overheating” only observed when we started the engine again to motor sail from Bonaire towards curaçao.
Yesterday I conducted a few more tests:
First, I unscrewed the sensor from the engine and submerged its tip on a small container with hot water at 160 F degrees. When I turned on the engine switch it was reading 200 F. So that confirmed that it had to be either the sensor or the gauge, at least I though. However when I dismounted the instrument panel to check if corrosion was involved in the problem, the temperature readings became erratic going from 120 to 220 up and down depending on how I moved the cables behind the panel. I went on and cleaned al the connections I could find and after fiddling with the cables the temperature of the water and that of the gauge coincided in a systematic manner.
CONCLUSION: the engine was never overheating. The sensor and the gauge were OK. The reason for the bad reading was corrosion on the cables behind the instrument panel. No need to change the gauge, or the sensor, I am just going by buy a new set of cables and two gun infrared thermometers!
I hope the this may help others when they have a similar problem
Thanks to all for providing very helpful suggestions: