A potentially significant consequence of the dynamics due to particles interacting electromagnetically with electromagnetic zero-point plus Planckian radiation is the prediction of a stochastic acceleration mechanism. For particles without constraining forces or other collision mechanisms present, such as due to the walls of a container or to interparticle collisions, this mechanism results in average speeds that continue to increase with time. This secular acceleration effect has been proposed and analyzed in the past by Rueda and others [A. Rueda, Space Sci. Rev. 53, 223 (1990)]for being a possible source for cosmic-ray production; other possible astrophysical consequences have also been examined. However, the thermodynamics of secular acceleration have presented conceptual problems, such as the apparent source of continual average energy extraction and the possible violation of the second law of thermodynamics. These concerns are examined in detail here, with the conclusion that secular acceleration does not appear to violate these basic laws.