how to calculate solar panel size needed to run circuit
If I understand you correctly, you have only 5 x 5 inches for solar panels?  That would translate to approximately 5 watts if I remember correctly (I will check that figure and edit if necessary). EDIT: 6 x 6 inches will give you 4 watts for the average solar cell under full sunlight. 

It is unclear if you plan to run your heater at the full 4 watts, but if you do, then for how long?

If your panel puts out 4-5 watts and your heater uses 4 watts, then you just need to find out how much sunlight you get and if it is enough.

By the way, most 12 volt lithium batteries would be 12.6 volts fully charged.

Good luck.