Summary: It is shown that a generalized formulation of statistical mechanics provides a unified logical basis for the construction of a manifestly covariant theory of relativistic thermodynamics in contrast to heuristic approaches, such as the original theory by Planck and Einstein, and more recent ones by Ott and Møller. The generalized formalism is applied to discuss the relativistic thermodynamics of blackbody radiation, including such processes as the absorption and reflection of a light beam as well as the adiabatic cooling of cosmic blackbody radiation in Milne's model of the universe. The measurement of the temperature of a light beam is also discussed.