Birds and mammals are both endothermic, meaning they metabolically generate the heat they need to keep their body within a certain temperature ranger.
But birds are closer relatives to reptiles than they are to mammals, and reptiles are not endothermic. Thus birds and mammals developed endothermy independently; and here is the question:
How does thermal regulation differ in birds and mammals?
This is in between a comment and an answer...
Notes
You probably meant "evolved" instead of "developed".
Thermoregulation is performed by a set of different mechanisms and it is plausible that your question would be considered as too broad. Note however that I am NOT a physiologist and might overestimate the scope of the question.
Similitudes between birds and mammals
From wikipedia (here)
In cold environments, birds and mammals employ the following adaptations and strategies to minimize heat loss:
- Using small smooth muscles (arrector pili in mammals), which are attached to feather or hair shafts; this distorts the surface of the skin making feather/hair shaft stand erect (called goose bumps or pimples) which slows the movement of air across the skin and minimizes heat loss.
- Increasing body size to more easily maintain core body temperature (warm-blooded animals in cold climates tend to be larger than similar species in warmer climates (see Bergmann's Rule))
- Having the ability to store energy as fat for metabolism
- Have shortened extremities
- Have countercurrent blood flow in extremities - this is where the warm arterial blood travelling to the limb passes the cooler venous blood from the limb and heat is exchanged warming the venous blood and cooling the arterial (e.g., Arctic wolf[3] or penguins[4][5])
In warm environments, birds and mammals employ the following adaptations and strategies to maximize heat loss:
Behavioural adaptations like living in burrows during the day and being nocturnal
- Evaporative cooling by perspiration and panting
- Storing fat reserves in one place (e.g., camel's hump) to avoid its insulating effect
- Elongated, often vascularized extremities to conduct body heat to the air
