Three different rules get mixed up here: one about the shape of his face, one about what his breed is allowed to do in law, and one about the weather on the day. Any of them can stop a move, and different people check each one at different points.
1. Snub-nosed breeds
Several airlines won't take snub-nosed dogs and cats at all, the breeds called brachycephalic. There's no single official list, because IATA names no breeds and each airline publishes its own, and the lists include cats as well as dogs. Examples people ask us about: Shih Tzu, Boxer, Bulldog, French Bulldog, Pug, Boston Terrier, Pekingese, Persian and Exotic Shorthair cats. IATA asks for a crate 10% larger for them, and for snub-nosed dogs to be stowed as far as practical from other loads in the hold.
2. Breeds many countries won't accept
Many countries won't accept breeds such as Pit Bull, Staffordshire Bull Terrier, American Bull Terrier, American Bulldog, Japanese Tosa, Dogo Argentino. If he's one of these, this is a conversation for before you choose a city, not after you've signed a lease, and we'll get the rules for the country you're considering in front of you first.
3. Heat
Airlines set their own temperature limits by carrier, aircraft, airport and route, and snub-nosed breeds often get tighter ones. In much of India that can close a good part of the calendar, so we check the whole route before a flight is chosen. More in heat embargoes.
And the one that applies to everyone
We don't sedate pets for travel, and here's why.
Source: IKAN Lola's published airline and breed restrictions, and IATA Live Animals Regulations, 52nd edition, Container Requirement 1 on snub-nosed breeds.