i would say earth fault or relay fault, the circuit as i understand it, basically decides what status the engine is in, ie cold or hot, this is determined by a coolent sensor, if coolent is cold, ths sensor doesnt ground one side of the relay, this fires the relay into action to power the glo plugs, if the coolent is warm then the reley does not energise and won't power the plugs.
if there is a break in the wire the connects to the coolent sensor then the relayand light will stay on for around 90 seconds and slowly burn out the plugs. So get it looked at asap IMO
so your circuit is kinda working, so bad earth or faulty sensor, maybe faulty relay.