Is cooking already thawed-out ready meals using a food warmer safe?

I have one of those Hot Logic food warmers that is designed to heat up food when you are camping or something. I will be camping for 4 days and I want to use this thing but I'm starting to realize that it might not be safe as far as bringing these ready meals that I want to make in it. 

They say on the instructions of ready meals that you need to cook them from frozen but since I will be camping, they will most likely thaw out, I don't have a way to keep them frozen the entire 4 days. I can put them in a small cooler bag with a freezer pack but from experience that has never kept anything frozen and I'm lucky if the things are still cold 3 days later.

So I want to buy some of those single serving ready meals and bring them camping and warm them up in this food warmer but chances are they will be thawed out before I can cook them. This doesn't seem safe according to the instructions on the boxes.

Does anybody else have one of these food warmers? Do you think it would be fine to heat up these meals if they have been thawed out for a few days?