The heater just keeps running. Firstly, the lead will start to heat up as the heater never reaches the thermostatic cut-out temperature. This is because it's trying to warm too big an area and it can't cope.
After the lead has been heating for a while it will then heat the plug up. This then causes the plastic socket to expand and crack. If left long enough the plug will start to burn, as will the socket.
Eventually, it will start a fire.