1) panting--increase air flow over respiratory surfaces. This requires energy.
2) gular fluttering--has been described in 150 species of birds. Pelecaniformes' loose, thin pouch at floor of mouth can flutter with little energy to increase airflow in mouth. Gular pouches weigh little and show resonant properties. (Panting increases with heat while gular fluttering remains constant regardless.)
3) urinate on legs--done by storks and turkey vultures, this obviously increases evaporation rate on legs.
4) increased efficiency of water conservation--(e.g., kidney efficiency improvement)--desert birds (like Roadrunners) have longer loops of Henley than do non-desert ones, which may lack them. Look these up if you don't know what they are or how they work.
5) behavior. Birds often dangle their legs behind them as they fly in high temperatures. Sandgrouse: daily activities correspond to cooler temperatures; feathers absorb water, which can be transported to their young. Most desert passerines thermoregulate behaviorally. Magpies face white parts of their body towards the sun when then are hot, black parts when they are cold.
6) countercurrent exchanges are lacking when birds need to loose a lot of heat. Maximal heat loss is through feet (like Snowy Owls).