Although birds do not possess sweat glands, they do lose heat by evaporation from moisture on the skin and by panting. The ambient temperature and relative humidity plays a role in how much heat is lost this way. The transfer of heat by radiation, conduction, and convection always goes from a higher temperature to a lower one. Radiation requires no contact and is the reason why the sun's rays feel warm and why a room feels colder than the thermometer reading when the walls and floor are cold. Conduction transfers heat by direct contact.
Conduction is very rapid if the temperature difference is large.
This is why a cold water bath makes us feel cold all over very quickly and why it is not advisable to lick a frozen object. Convection occurs when heat is carried away by the movement of the air. It takes a lot of food to sustain life in a cold environment. Birds, with their high body temperature and high metabolic rate eat more food, ounce for ounce, than most other vertebrates, shrews being the exception. Birds tend to be very active much of the time.