ardly:
I think the Arduino should be able to turn the radiator on, 'plot' the rate of change of room temperature and switch off so that the target is hit with acceptable accuracy.
That's a very interesting idea. However I wonder if it would only be practical when there is a large difference between the actual and the desired temperature.
But that, in turn, raises a question that we have not yet asked the OP. Is his desire for fast and accurate heating only required for the initial rise in temperature from cold to normal?
Because the concept of fast seems unlikely to be relevant once the room has reached the desired temperature. Which makes me wonder how much trouble it is worth taking with the fine control of the temperature for a single event - perhaps just once or twice per day?
...R