The relaxed eddy accumulation (REA) method is an attractive alternative to the eddy covariance method to measure trace-gas flux, because it allows the use of analyzers with an optimal integration time to reduce the noise. However, the use of an empirical coefficient b results in uncertainties in the REA method. The consistency of b for temperature was investigated using a 1 year dataset obtained at three forest sites in East Asia: a temperate evergreen coniferous forest, a tropical evergreen broadleaf forest, and a cool-temperate deciduous coniferous forest. The observational b ranged from 0.54 to 0.57 under unstable conditions. Although the values for observational b were within narrow ranges among the sites, there were slight site-specific differences. We introduced new expression of b, similarity b, based on scalar similarity using the integral turbulence characteristics to investigate the nature of b. Both the observational and similarity b increased with increasing atmospheric stability under stable conditions, when lower values for the standard deviation of the vertical wind velocity resulted in higher values for b. The variations in b under stable conditions differed among sites. There were no seasonal variations in the observational b at all sites. Consequently, the present study recommends determining the coefficient b for unstable conditions for each site and considering changes in b associated with atmospheric stability in order to minimize errors in the REA method.