Worried Dog,
The aircraft has a specific hold for carrying 'livestock' (Cats, dogs, sheep (NZ)). When we are notified by NOTOC (See above) then the heating and airflow to that specific hold (on the Boeing 777) are increased to ensure the animal is comfortable.
Personally I always check that the livestock has been loaded into the correct hold and well/sensibly secured. For example a dog box next to/facing a cat box is not sensibly secured! Common sense in most parts of the world but sadly not in some.
Your pets will be in the best of hands!