Repeatability of a trait estimated over long time intervals and its heritability make it possible to assess whether it can serve as an individual characteristic and be subject to selection. Heritability and repeatability of energetic traits are still poorly studied in birds. The most important physiological characteristic of the homoiotherms is the minimal level of energy expenditure, referred to as the resting metabolic rate (RMR), which, in the absence of the expenditure for biomass growth, does not exceed the basal metabolic rate (BMR). We have estimated the BMR repeatability in adult free-living pied flycatchers in Moscow-region (55°44′ N, 36°51′ E; 1992–2008) and Tomsk (56°20′ N, 84°56′ E; 2008–2009) populations over intervals of 40 days to 3 years. In the Moscow-region pied flycatcher population, the BMR repeatability recorded during the same period of the reproductive season was τ = 0.34 ± 0.10 for a 1-year interval (n = 80), τ = 0.60 ± 0.15 for a 2-year interval (n = 19), and τ = 0.85 ± 0.13 for a 3-year interval (n = 6). In the Tomsk population, the BMR repeatability for the 1-year interval was τ = 0.49 ± 0.11 (n = 50). The repeatability of a trait is a measure of its constancy in time and specifies the upper limit of its heritability. RMR heritability was assessed in cross-fostering experiments in the Moscow-region free-living pied flycatcher population in 2003–2005. The RMRs of chicks and BMRs of their biological fathers displayed a positive correlation, whereas no correlation was found between the RMRs of chicks and their foster fathers. The RMR heritability value was h2 = 0.43 ± 0.17 (n = 210). The obtained estimates for repeatability and heritability of fundamental energetic traits in pied fly-catcher are rather high for a physiological trait and suggest the existence of evolutionary stable diversity of the avian population in the BMR.