In this paper, we study the thermalization process of an enclosed fluid mixture near its liquid-vapor critical point subjected to cross-boundary mass diffusion. We reveal that the mass piston effect, a fast and efficient thermalization phenomenon can take place, as a result of three cooperative or competing mechanisms: the boundary velocity, the Dufour effect, and the concentration variation. We propose a theory to formulate the mass piston effect on the acoustic timescale, including the amplitudes of the acoustic wave, the wave's propagation, and the energy and temperature efficiencies measuring the performance of the mass piston effect in terms of energy transfer and thermalization. We apply our theory to the representative C2H6 - CO2 mixture, and present the behavior of various thermodynamic indicators in the critical region over the whole concentration range. We identify that the boundary velocity is the main factor that restricts the efficiency of the thermalization. By comparing with numerical simulations of different initial states and boundary conditions, the theoretical predictions are quite satisfactory. The current work adds a new member to the family of piston effect and gives new insights into the thermalization process in the critical region. (C) 2019 Elsevier Ltd. All rights reserved.