According to the manual !!
TRANSMISSION TEMPERATURE SENSOR
The TRS has an integrated thermistor that the PCM/TCM uses to monitor the transmission’s sump temperature. Since fluid temperature
can affect transmission shift quality and convertor lock up, the PCM/TCM requires this information to determine which shift schedule to operate in. The
PCM also monitors this temperature data so it can energize the vehicle cooling fan(s) when a transmission “overheat” condition exists. If the thermistor circuit
fails, the PCM/TCM will revert to calculated oil temperature usage.
CALCULATED TEMPERATURE
A failure in the temperature sensor or circuit will result in calculated temperature being substituted for actual temperature. Calculated temperature is a predicted
fluid temperature which is calculated from a combination of inputs:
² Battery (ambient) temperature
² Engine coolant temperature
² In-gear run time since start-up
so check if fans are cutting in ??
Oil gets less viscous as it warms up .. I imagine this would cause slip rather than not changing up but I may be (and probably are) wrong.
If `the temp is out of range I would imagine you would get a OBD error code,although there is no mention of this in the 41TE section of the worksh*t manual .. check for error with key dance.
Also can find no mention of acceptable temp range - sorry.
Also, good to identify your vehicle as you may not have a 41TE box........