Can't be heat, the supply pump is transferring cold water!
I'm not sure if your machine works this way but with mine, if the machine is switched off and you turn the ignition one click over, it will send electricity to the supply pump. You could do that and see if it is running.
The other thing to check is your float valve in the header tank, it may be stuck closed. Give it a jiggle up and down a few times, it may have a bit of scale stuck in it or something!