The paper reports on numerical simulation of a laminar near-wall flow subjected simultaneously to a favorable pressure gradient and wall heating at a constant temperature. An important feature of such a flow is an overshoot of the streamwise velocity profile when the velocity within the boundary layer exceeds the velocity in the external main flow. It is shown that the overshoot appears due to the simultaneous action of wall heating and acceleration. The investigation shows that the maximum velocity at a finite Reynolds number arises when the acceleration parameter is positive and the ratio of the wall temperature and the free stream temperature is greater than unity. The overshoot causes an increase of the skin-friction coefficient and the Stanton number. In addition, it leads to a negative momentum thickness. The article demonstrates the applicability of the approximate formula by Volchkov (2006) for the evaluation of the maximum velocity. Based on the own recent research and on an overview of the published literature on similar and related flows, it is concluded that the main prerequisite for a velocity overshoot is an input of energy from a bounding wall. (C) 2014 Elsevier Ltd. All rights reserved.