The thin heating element is used in electric heater and the filament of the bulb is also thin.
Since, a thin wire has less radius than the thick wire. So, it has less area of cross section than the thick wire. As we know, ​resistance of the wire is inversely proportional to area of cross section of wire. So, a thin wire has more resistance as compare to thick wire. So, in order to get more value of resistance, the heating elements are kept thin.