We use dry ice in our delivery boxes. Dry ice does not melt the same way that regular ice does. It "sublimates" (going from frozen solid to gas without turning into a liquid)! Dry ice can last 18-36 hours and your food will still be frozen for awhile after that.
As long as your food is still mostly frozen or cold (40F), it is safe to refreeze and then prepared per the instructions on your meal.