Hello Peter,
...Even a brief burst of acceleration doesn't reduce the engine speed...
I suspect that what you mean is that the engine speed

returns to a too-high value even after the foot has been taken off the accelerator.
This strongly suggests the temperature sensor, as Ulf already mentioned. Does your car also take a longer time to warm up when it's in this state?
In the event of a detected sensor failure, the control unit assumes that the engine is cold, initiates the glow plug system (which normally only activates below 10.5°C), and increases the idle speed.
It's possible that the transmitter is experiencing a short circuit or an open circuit to ground at certain temperatures.
Best regards, Rudi.