I'm not claiming any medical reason to avoid drinking hot water, I'm not a trained medical person. I just know that it makes me feel ill. Froze, do your wrapped bottles still fit in a regular cage? If you can save some weight, that could help. Though my complete rig, bike+gear+shared+food, came in around 85#, which was towards the low end of my group's weights.
4 of my cages are the Arundel Looney Bin cage, these are adjustable, if you tried to put a 24-ounce bottle with that wrapping a regular cage could rip it unless you can spread it apart with your hand first, but with the Arundel I just open the cage up larger.
I use the Arundel cage so that those bigger 52-ounce bottles I use will fit on the front, and so that I can place the two plastic insulated bottles into the cage without ripping the wrap, but that does mean that when you need a drink you'll have to stop and turn the dial on the cage to open it up so you can pull it out with ripping the wrap.
Another reason for Arundel cage is so that it's impossible for a bottle to eject, and if I want to stick some other sort of bottle into the cage it will fit most bottles.
My only "normal" non-adjustable cage is the one on the underside of the down tube that holds a 16-ounce bottle due to any larger bottle hits the front fender.
I do carry a bit of spare AL foil just in case one rips, but so far that hasn't happened.
I used to use 4 stainless insulated bottles, another reason for the Arundel cages, in my search to find ways to reduce my carrying weight that was one of the things I had to change.
Also, I discovered that I can carry 11 more ounces in each front bottle cage using plastic bottles, that's 22 more ounces of fluid than the largest stainless that I could find that would fit in the Arundel cages. So I killed two birds with one stone, less bottle weight, more water, but even with the more water weight, it still is less weight than the stainless bottles.
By the way, I carry this much water because I'm bike camping, not on a 2-hour ride! So I might be riding for 4 to 6 hours at a stretch, then need water for food preparation at the campsite.