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 , where tD is the thermal diffusion relaxation time and γ0 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, . Furthermore, it shows that tE 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.