I'd use a heat pack. Look what the temp is at the HUB (UPS hub is in Louisville KY) and then look at the temp in the early morning of the destination city.
A heat pack will raise the temp in the box about 15 degrees
If it were a montane species I would not use a heat pack if the low was 45. If it was a lowland species I would wrap the heat pack up well with news paper so it doesnt put out a ton of heat. Tape the heat pack at the top of the box. Do not set the animal above the heat pack. Make sure you poke holes in the box also. I usually poke a hole, with a pen, in all the corners on the bottom. After I tape it shut I carefully do the same to the top. I would also not recommend using a deli cup when using a heat pack. Heat can build up in a box and then even more inside the container. I know a few cases of animals showing up somewhere cooked. I would use a paper bag or cloth bag. This method works great for me and lots of others but some are successful using a container even when shipping with heat packs. You just have to do it right
Is this for a chameleon? If so, then I agree with Cain. It also depends on if the animal is being picked up from the hub or going out to a house. It also depends on if the animal is being trucked to the destination or if it's going by plane.