Check the fuse anyway just to be sure but if the fuse is OK the next step is to remove the cigarette lighter and see if it has power and ground to the heater element.
Could the cigarette lighter outlet have been damaged due to use of a MP3 player, phone charger, or radar detector chord?
My lighter was not working in my car so I check the fuse and it was good. My next step was checking the socket it had no power so I pulled the socket out and checked the wires and the two wires running to it had power. I found that there was a tiny black wire on the back of the socket that I figure was a fuse wire that melts when a device is left in the socket for a long period of time as a safety. I remove the wire from the two post and wrapped a small piece of wire between the two post that solved the problem.