More than likely not. Solar panels can produce way more than 12 volts. You could do it if you ran your panel through a charge controller, into a battery, then to your heater. However my experiences with 12 volt car heaters is that unless your room is very small, it might not produce enough heat to make a difference. Hope this helps.
If your 12 volt car heater is a 250 watt heater than your solar panel has to be a 250 watt or a bit bigger panel to maximize the heat output.
The solar panel and the heater need to stay hooked up, if you would turn your heater off and the fan is still running it would burn the fan motor up because the panel voltage will go up because you made the system unbalanced. You could however just turn your solar power of or disconnect the whole heater from the panel. No extra load should be hooked up to the same panel-heater circuit, this would decrease the panel voltage because again....the system is getting unbalanced. Clouds or dirty panels ect will lower panel voltage and amps and will lower the power output. for example ...if your 12 volt heater is hooked up to the panel and lets say that it is cloudy and the panel voltage dropped to 6 volts under load that would mean that the power output from your heater is now 62 watts instead 250 watts. The wire for 250 watts need to be a #10 wire and run it as short as possible. The fuse need to be a 25 amp fuse......do not use an automotive fuse, they get hot and may start a fire. Max current/amps on a #10 wire should be kept at 30 Amps or lower. If your run is long than you need to step up your wire size. To be honest, a 250 watt automotive heater is not much heat, unless you have very good insulation and/or a very small room. But heck, anything is better than nothing. You may consider air circulated solar panels that you can build with soda cans. Look it up at you tube.