I have checked the workshop manual and it is not mentioned anywhere at which temperature level the low speed and high speed should kick in.
As the 97°C kick in for low speed you mention is reported by the Engine ECU it can't be a temperature sensor problem.
The temperature sender is just a NTC resistor (NTC stands for Negative Temperature Coefficient)
The resistor decreases with higher temperature and the Engine ECU just measure the resistance and use a look-up table to convert the resistance to a temperature.
A certain resistance corresponds to a certain temperature
So it seems the software in your Engine ECU is set to enable the low speed fan when the Engine ECU measure 97°C cooling water temperature.
As the temperature sender includes a second NTC resistor for the gauge there can be a mismatch between the temperature reported by the Engine ECU and the temperature shown on the gauge.
I can try on my own 2.5 V6 to see at which temperature level the low speed kicks in.
My Car is a CF3 version, has only 1 temp sensors that is sending to the ECU and the Gauge,also i changed it 3 times and same issue even the gauge i just changed it, the previous owner sold it for this issue, and i thought its something i can fix
but i think this will kill me before i fix it