Been more than one frozen cat or dog, it does happen. The cargo areas are pressurized, but depending on the aircraft, usually only one area is heated for animals and other temperature sensitive items. In a Boeing 757 and 767 its the aft most bin area, know as the "bulk" bin since it is the area where loose cargo is loaded. Other bins get some amount of heat, but not much. The airplane is insulated, but the cold still soaks thru.
The batteries are mounted between the cargo bin sidewall and the outer skin of the aircraft usually (the APU battery in the aft bin).
The battery selection is based in large part on capacity of the battery. In event of electric failure, the battery must be able to power certain critical circuits for a given period of time, 30 minutes If I recall. Given all of the electric gadgets in the 787, there is a greater need for power, just for the essential stuff in an emergency, hence a more powerful battery is needed. I suspect Boeing went with the Li-ion battery to keep the weight down and still maintain capacity (amp/hrs) LiSO2 batteries have been banned in aircraft for some 30 years now. I don't know how different a Li-ion battery is, but its not uncommon to have a laptop catch fire, or a cell phone, when the sophisticated circuits that control the charge rate and such fail.
Too much new technology in one aircraft.