Remember that your goal is to get the cider inside the bottles up to pasteurization temperature (e.g., 180 F) and keep it there for some length of time (20 minutes?).
I think the hard part will be figuring out how hot to make the water you add to the cooler to allow for how much it will cool down due to the cooler bottles. (Wow, I used "cool" a lot!)
What I mean is, if you want to hold the cider in the bottles at 180 F and the bottles start at room temperature (say 70F), you may need to add a few gallons of boiling hot water (212 F) to have the whole system come to rest at 180 (i.e., the cider temperature inside the bottles at 180). Will the bottles survive this kind of shock? I think you'd be better off putting the bottles in a stockpot with water and bringing the whole thing up to your desired temperature. If, at that point, you want to dump it all in a cooler, fine, but why bother?