What kind of motor would I need to turn this central heating valve?
I once visited a hackerspace that was trying to make a light bulb throb between bright and dim for a replica TARDIS. Their solution was to get an ordinary dimmer, such as you'd mount in your wall, then mechanically link this to an RC hobby servo controlled by an Arduino.

It worked, for a few hours. Then something would break, every time.

Then, I showed them how to put a triac on an ATtiny. Not only was this solution about three orders of magnitude cheaper, it never broke.

Here's the lesson: just because you do something with your hands doesn't mean a machine should. This is why industrial automation robots look like this:



and not like this:



There are machines designed to control the flow of heated water to your radiator, and they don't look like hands to grab the knob that's already there. By searching for "electric radiator valve", I found this, available from decorisland.com:



It looks like the interface is two wires, and you apply a voltage to open the valve. This should be pretty easy to interface with an Arduino. But, it's also probably compatible with a standard wall-mount thermostat. You could even get one of the many internet enabled thermostats on the market (such as by Honeywell or Nest) and skip the Arduino, avoiding this problem: