Hello Peter,
...Even a brief acceleration does not lower the RPM...
I'm guessing you mean that the engine speed also remains at a high value even after you take your foot off the accelerator
This strongly suggests - as Ulf has already said - that the temperature sensor is the likely culprit. Does your car also run hotter for longer when it's in this condition?
The control unit, however, assumes that the temperature is cold if a faulty sensor is detected. It also preheats (which only occurs at temperatures below 10..5°C), and increases the idle speed.
There is a possibility that the source has a disconnection or short circuit against ground at certain temperatures.
Best regards, Rudi