Is the baggage compartment of commercial aircraft pressureized and heated?

Yes & Yes. Most aircraft send heated air into the main deck cabin and then passes through slots in the floor down into the lower cargo decks. It is common to carry pets and live animals in the lower cargo decks. Cargo aircraft, such as those flown by FedEx, carry flowers and live animals such as cattle. For special live cargo such as race horses, they will install compartment stalls and a seat for the trainer(with a portable oxygen bottle) so he can keep the animals calm.