My first transport took me to SC for two 50lb. ea. dogs. After lining the plane with plastic and towels, I figured I only added to the heat problem.
Put flexible ice packs on half of the laydown area under the blankets. This allows the dog to lay on them completely, or not at all. Any position can be taken so they will stay cool. I did not see heavy panting on my fuel stop at 90F during taxi.