Well , it will work but can't draw as much heat as required. As the supply is less than half of the heater requirement , the current drawn will also be less than half of required value ( according to ohm's law I=V/R ) . The heat or power will be 1/4th ( as P=V^2/R ) of the required heat. So the heater can't produce desired amount of heat .

Short circuit will not happen but the device will not give the desired o/p however in the reverse condition ( i.e. 110 volt heater and 240 volt power supply) there are chances of short circuit and melting of device.