Several airlines, including American and Delta, do offer a pet-check option, in which your pet can travel below-cabin on the same flight as you. In this case, the below-cabin area where your pet will travel is a temperature-controlled and pressurized environment.
Most major airlines do allow smaller pets to travel in the cabin with you. Your pet must be well-behaved, and able to fit comfortably in an approved pet travel-carrier that can fit under the seat in front of you.
American Airlines Cargo - Shipping Animals
Airline Pet Policy American - Fly Your Dog or Cat Safely - Pet Travel
Unless a pet is proven in advance as an emotional support animal or clearly a service animal for the blind or handicapped, weight and size restrictions apply to pets brought onto airplanes. Southwest Airlines doesn’t publish weight restrictions, but the cat or dog must fit in an approved pet carrier in which the animal can comfortably move around; the carrier also must fit underneath an airplane seat. American Airlines requires that the carrier be no more than 19 inches in length, 13 inches in width and nine inches in height; also, the pet and its carrier can weigh no more than 20 pounds total.
Airline Requirements for a Pet Carrier | USA Today
– To ensure your pet isn’t exposed to extreme heat, American Airlines imposes an embargo any time the current or forecasted temperature is above 85 degrees Fahrenheit at any location on the itinerary. However, if your pet fits in an approved carrier that can be placed under your seat, he can travel with you in the cabin.• AIRLINE APPROVED PET CARRIER: Size Meets Most Major Domestic Airlines In Cabin Requirements, such as United Airlines, American Airlines, Southwest …