Final answer:
Smaller cells tend to lose energy as heat more rapidly than larger ones due to a higher surface area to volume ratio. This results in smaller organisms having higher BMRs to maintain their body temperature, impacting their distribution in different climates.
Step-by-step explanation:
Smaller cells are more likely to lose energy as heat to their surroundings when compared to larger cells. This phenomena is explained by the surface area to volume ratio. Smaller organisms have a relatively higher surface area compared to their volume, which facilitates a more rapid heat exchange with the environment. On the other hand, larger organisms with a smaller surface area relative to their volume lose heat more slowly, allowing them to maintain their internal temperature more effectively. When considering shape, spherical bodies which have the least surface area per unit volume will heat and cool more slowly. Conversely, a filamentous shape, with a greater deviation from a sphere, will gain or lose heat more quickly.
Due to these principles, small endothermic animals with a high surface area relative to mass will have a higher basal metabolic rate (BMR) per body weight to offset their quicker loss of heat. On a broader scale, this also implies that we would not typically find very small warm-blooded animals like mice in extremely cold environments such as the polar regions, because they would lose heat rapidly and require a tremendous amount of energy to maintain their body temperature.