In this paper, flow and heat transfer characteristics of an unsteady rear stagnation-point flow over a moving wall with transpiration are studied. The flow solution is an exact solution to the unsteady Navier-Stokes equations. By ignoring the viscous dissipation terms, analytical solutions of the boundary layer energy equation are obtained for the cases with a constant wall temperature and a prescribed time-dependent wall heat flux. The effects of the controlling parameters on the solution domain, the velocity distribution and the temperature distribution in the fluids are analyzed. With certain given values of the controlling parameters, two solution branches are found for both the flow and the heat transfer problems. These closed-form solutions are rare and can be used as a benchmark problem for numerical code validation. (C) 2013 Elsevier Ltd. All rights reserved.