The heat transfer problem of a body moving in opposition to a flowing fluid in a channel is investigated numerically. This problem belongs to a class of the moving boundary problems and an arbitrary Lagrangian-Eulerian method with a Galerkin finite element method is adopted to analyze this problem. Several different moving Velocities of the body and Reynolds numbers are taken into consideration. The results show that the fluid simultaneously replenishes the vacant space induced by the movement of the body and new recirculation zones are formed around the body. These phenomena are quite different from those of the body fixed in the flowing fluid. Heat transfer rates of the body are enhanced remarkably as the body moving in opposition to the flowing fluid. In the computing range, the mean global Nusselt number Nu can be estimated by an equation of 0.664(Re V-b)(1/2) - 1.34.