The heat transfer near the critical point is governed not only by diffusion, convection, and radiation, but also by a thermomechanical coupling called the Piston Effect. This fourth mode of heat transfer is responsible for the so-calledcritical speeding up, which contradicts the first expectation of a critical slowing down of the heat diffusion. So far, the viscosity has been neglected in all the existing theoretical models of the Piston Effect. The aim of this paper is to present a comprehensive model of the Piston Effect, written for a real-fluid equation of state and including the critical divergence of the bulk viscosity. It is shown in particular that when the critical point is neared, the heat transfer goes faster and faster, until a point is reached where viscous stresses are no longer negligible. When going closer to the critical point, the heat transfer then slows down again; a regime ofcritical slowing downis entered. This phenomenon should happen sufficiently far from the critical temperature to allow experimental checks. Moreover, it could be used as an indirect way of measuring the critical divergence of the bulk viscosity. ©1998 American Institute of Physics.