An approximate solution of the classical thermodynamic model for compressible heat transfer of a quiescent supercritical fluid under microgravity leads to the well-known piston effect relaxation time $tPE=tD/(\gamma 0\u22121)2$, where *t*_{D} is the thermal diffusion relaxation time and *γ*_{0} is the ratio between specific heats. This relaxation time represents an upper bound for the asymptotic bulk temperature behavior during very early times, which shows a strong algebraic relaxation due to the piston effect. This paper demonstrates that an additional relaxation time associated with the piston effect exists in this classical thermodynamic model, namely, $tE=tD/\gamma 0$. Furthermore, it shows that *t*_{E} represents the time required by the bulk temperature to reach steady-state. Comparisons with a numerical solution of the compressible Navier–Stokes equations as well as experimental data indicate the validity of this new analytical expression and its physical interpretation.