Polar bears (Ursus maritimus) face extremely cold temperatures and periods of fasting, which might result in more severe energetic challenges than those experienced by their sister species, the brown bear (U. arctos). We have examined the mitochondrial and nuclear genomes of polar and brown bears to investigate if polar bears demonstrate lineage-specific signals of molecular adaptation in genes associated with cellular respiration/energy production. We observed increased evolutionary rates in the mitochondrial cytochrome c oxidase I gene in polar but not brown bears. An amino acid substitution occurred near the interaction site with a nuclear-encoded subunit of the cytochrome c oxidase complex, and was predicted to lead to a functional change, although the significance of this remains unclear. The nuclear genomes of brown and polar bears demonstrate different adaptations related to cellular respiration. Analyses of the genomes of brown bears exhibited substitutions that may alter the function of proteins that regulate glucose uptake, which could be beneficial when feeding on carbohydrate-dominated diets during hyperphagia, followed by fasting during hibernation. In polar bears, genes demonstrating signatures of functional divergence and those potentially under positive selection were enriched in functions related to production of nitric oxide, which can regulate energy production in several different ways. This suggests that polar bears may be able to fine-tune intracellular levels of nitric oxide as an adaptive response to control trade-offs between energy production in the form of ATP versus generation of heat (thermogenesis).