[Ian M Davis]

Because the thermostat is removed the temperature stays always 60˚C. I measured the resistance on the temperature sensor while showing the STOP; not the ECU.

Okay I think I understand. If the sensor is 5 kOhms at 25˚C the 1.5k to 2.0k range seems about right for a coolant temperature of 60˚C. I understand from your original comment that the fault clears if you recycle the battery connection. While it's unusual all the evidence is pointing to a fault inside the engine ECU. One further check worth doing is to measure the battery voltage when the engine in running. I would expect around 14 Volts. A higher voltage may damage or overheat the ECU.

One warning if you want to change the ECU you can not just get a unit from another car. The ECU and BSI are a matched pair so if you just change the ECU the immobiliser will not unlock the ECU. The simplest thing is to change the BSI, ECU and Key PCB with a set from an identical car. Alternatively, there are some specialist companies that can clone your existing ECU or sell you a modified ECU where the immobiliser is disabled (i.e. unlock).