I did a Google for programmable thermostat with remote sensor, however most the sensors seemed to be for under floor heating so the floor does not get too hot.
I am sure they are made, but to get the timing and the remote in one sensor seems to be a problem.
I used thermostats to control my beer brewing which can handle 13 amp they are also used for reptiles, and can be bought as plug in devices, but it would mean two devices one for time and one for temperature.
When I get to PC I will see if I can find a link. With water easy fit a programmable TRV.
The Inkbird ITC-306 is a plug in thermostat with a sensor so sensor can be in bathroom but thermostat in the location where plugs are allowed. When I came to do beer the 306 was not around, so use an STC-1000 there are many more plug in devices
where the sensor is not part of the thermostat.
This advert seems to do what you want but I can't find the current rating, and this is the problem, loads of devices where the sensor is battery powered so OK in a bathroom, but most seem to be limited to 3 amp. So not really suitable for a towel rail.
There are
Specials designed for a towel rail note 800 watt only.
This is designed again for a towel rail however to work it would need to be in same room as towel rail.
This seems to show what you want But £100 + £33 is an expensive method to control a towel rail, it would take many years to get that back in saved electric.