Last winter the heated rear screen stopped working in our 2006 Ford Mondeo - the 30A fuse had blown. I fitted a replacement (JCASE female type) but when the screen was turned on the fuse blew again. The heater is formed of wires attached to the inside surface of the screen (not embedded in the screen) and all of them are intact, with no visible short circuit.

The local Ford dealer was unable to find a reason for this problem. I did an investigation of my own with a multimeter and found that the heater works if the engine is not running. As soon as the ignition key is turned (current to the starter) the fuse blows. Can you think of a reason for this problem and what I might do to solve it?