You've answere your question there.
Sounds to me like a faulty room thermostat.
But first, check the radiator valves are turned up full. If still no heat, then its the room stat. They should always click at room temperature (no matter how warm or cold the room is), if it don't click,...its a short circuit.
Be sure to write down the Manufacturers name, and model name/number of the stat and try and get the same model. (this is so you can get like for like and slot it straight in, and not worry about rewiring the wall plate/base). Take the details into any Parts Center/Plumb Center and they'll sort you out. Usually anything up to £30.
Good luck.
Northern Knight, February 2010