If it's not to late, I have the same problem with my RT.
The control box contains 3 resistor
and 1 thermal fuse, the thermal fuse has ruptured (they are prone to ageing) and I'm reasonably confident that this is what the original posters problem is.
You can check it by bypassing the fuse with a piece of wire.
The good news is that they are available from Maplin for 49pence!, the bad news is they come in a variety of temp settings and I can't see any markings on the original!
Does anyone know what value is needed or can anyone have a gander in an old unit and read any surviving markings on the fuse?
The fuse looks like a resistor with one pointy end and an unburnt one will be silverish. It is found under the resistors and at right angle to them.