10 50 90 130 170 M/m 0.5 1.5 2.5 3.5 4.5 T$_{P}$/T$_{L}$ FIG. 5: (Color online) Ratio of the temperature parameter of the piston, T$_{P}$ , to the granular temperature of the gas next to it, T$_{L}$ , versus the mass ratio M/m , for several values of the coefficient of restitution of the gas α , as indicated in the insert. The curves are guides for the eye. In all the cases, the coefficient of restitution for the gas-movable piston collisions is α$_{P}$ = 0 . 99. For instance, T$_{P}$ /T$_{L}$ decreases as M/m increases for α > 0 . 95, but it happens the other way round for α < 0 . 95. Actually, as α decreases below this value, the increase of the temperature ratio is rather fast, and T$_{P}$ reaches to be up to four times larger than T$_{L}$ . If the parameters T$_{P}$ and T$_{L}$ were interpreted as real temperature parameters, this latter behavior would be fully counterintuitive. The temperature of the heated body (the piston) is larger than the temperature of the heating one (the gas next to the piston). From the values of σ$_{Z}$ and ( ∂L/∂M )$_{v}$$_{W}$ obtained from the event driven simulation data, the effective temperature T$_{eff}$ has been computed by means of its definition, Eq. (12). In the Appendix some details are given of the way in which the above derivative was actually evaluated. Then, in Figs. 6 and 7 the temperature ratios T$_{eff}$/T$_{L}$ and T$_{eff}$/T$_{P}$ are plotted, respectively, as a function of the mass ratio for the same systems as in Fig. 5. A clear 14