Sounds like the thermostat is blown, allowing the element to keep heating until it burned itself out.
We had a engineer out today for another issue to do with the fan oven on our Smeg range cooker not maintaining temperature and he said it has happened on cookers he has attended.
Likely you'll need a new thermostat, a new fan element and possibly a new fan
Expensive, but better get someone qualified to look at it in case there is other damage.
Rob in Nottingham
November 2009