I've been thinking about the screen lighter. Sorry to be a party pooper, but I don't think it will work. The reason it works in you car lighter, is that the heating filament has relatively small cross section, giving it just the right resistance and low heat capacity. A screen, on the other hand, has many, many paths by which the current can travel, meaning you would have to have pretty darn high current to really heat up any significant area of screen.
Maybe I'm envisioning this wrong. You might make it work by constraining the current path to, say, a strip of screen, maybe 3/4"x5". Also, you have to remember that your car battery, while only 12V, is capable of wicked high current. If you're planning on making this thing plug-in (120V AC), you need a step-down transformer/rectifier to something safer, like 12-30 V DC. The expensive part is that it needs to be capable of high current (like at least 10A, maybe 25A to be sure it can handle it). Car/marine battery chargers/jumpers are often in this very bracket (or higher amperage). Another posiiblilty would be to just hook it up to a car battery, but then you'd have to charge it from time to time anyhow.
The heating will occur primarily at the highest resistance point in the circuit. Make sure this is your screen, and not your wires, connections, switches, or even your current source (transformers and even batteries have internal resistance). If you make sure the above is true (by a good margin), then the lower the screen resistance, the higher your current flow and the faster your heating will be.
If you use a current source in the range I mentioned above, decent gauge wires and high amperage switches, you might be able to do switch < wires < .01 ohm, and screen ~.5 ohm. You'll have to select your screen thickness (I mean how heavy the wire in it is), width, and length, to shoot for this goal.
Hope this helps (and I also hope that I'm not insulting your intelligence by posting it). Good Luck!