At very low temperatures, the bird shivers - involuntary muscle contractions generate heat production. Birds can behaviorally thermoregulate to some extent to reduce heat loss. The most conspicuous behavior is migration to a warmer climate. Or fluff feathers to trap heat. And Brown Creepers by the dozens huddle together for warmth at night.
Many mammals make use of burrows but only a few birds do -e.g.
The evolutionary reason is that, being unable to feed on insects and nectar in the darkness, the hummingbird would lose too much energy overnight. Respiratory evaporative heat loss - this is the most important form of heat loss in birds and virtually all birds exhibit some form of panting. The hyoid bone flexes and the whole area is suffused with blood. Wings can be held away from the body and the feathers elevated. Albatrosses raise their feet off the ground and spread their wings to shade their feet.