Variation in metabolic rate was based on relationship between three factors: body weight, food habits and the altitude at which the birds live.
Basal metabolic rate of birds is associated with temperature and precipitation, not primary productivity (White et al. 2006) -- Basal metabolic rate (BMR) represents a significant component of animal energy budgets, and is correlated with a range of ecological, physiological and life-history variables, as well as phylogeny. However, even after accounting for the effects of body mass, considerable interspecific variation remains, and understanding the causes and consequences of this variation is key to understanding how animals function in the wild and the limits that are set on their physiological performance.
The compensation and increased-intake hypotheses predict that basal metabolic rate (BMR) influences reproductive performance; if so, variation in BMR may be related to differences in individual quality.
A classic adaptive explanation for variation in BMR derives from the observation that species from hot arid environments have lower BMRs than species from non-arid environments. This is postulated to result from the need to reduce (i) the rates of endogenous heat production in hot environments where evaporative water loss is restricted by water scarcity, and (ii) the food requirements and energy expenditure in environments where resources are sparse and widely distributed.
Complementary to this, the high BMRs of species from temperate and polar latitudes are associated with high maximal rates of thermogenesis and increased cold tolerance.
In a countercurrent exchanger, flow in two adjacent tubes (like blood vessels) is in opposite directions. Imagine these are blood vessels in a bird's leg: the artery on top & the vein on the bottom. The artery is bringing warm blood into the legs, heat from the blood in the artery is transferred to the blood in the vein (but, of course, oxygen & nutrients continue on to supply the cells in the feet). As a result of this heat 'exchange', blood in the bird's feet is relatively cool & little heat is lost. So, even a duck standing on ice loses little heat from its feet.