how to calculate solar panel size needed to run circuit

Iam doing a project and want to calculate what size solar panel to use to run my circuit. the only thing is that I have some size constraints involved cant be bigger and $5\times5$ in. I have a 12.2V lipo battery that is going to be powering a 4W 12V DC heating element at $140^{\circ}$C. I think I need to add a voltage regulator because I want the temperature to be constant and no greater than $50^{\circ}$C. If some one could give me some advice in what to do I would appreciate it greatly.

• First head over to the physics forums and find out how much energy you need to heat your unspecified volume from ambient (also unspecified) temperature in the (yet still unspecified) time. Then we can know how you can best supply the power for that required energy. – Majenko Mar 10 '15 at 21:22
• A voltage regulator regulates voltage. If you want a constant temperature, you need a temperature regulator. In any case, you mention both 140C and 50C -- which is it? – Dave Tweed Mar 10 '15 at 21:58
• That's a lot of question. For a start try following the energy, with losses at each stage. 1.) how much light? – George Herold Mar 11 '15 at 0:33
• I will just point out that if you want to use solar power to heat something, it will probably be more efficient to use solar thermal collectors instead of photovoltaic. – mkeith Mar 11 '15 at 1:18