Temperatures above and below the range of thermoneutrality will both result in increased heat production. Thermoneutrality means that the conditions are such that the bird doesn't use energy to either lose or maintain body heat. If the temperature drops too low, heat production cannot be maintained and the bird dies. Birds die faster due to heat stress than cold stress. 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.