Steady state conduction of heat from a stationary wall to a medium moving at a uniform velocity is the subject herein. This medium can be a solid or a fluid moving at a constant velocity. The surface of this medium is insulated until a change in the surface heat flux occurs. The determination of temperature field is the main objective herein. The results show that the surface temperature begins to increase before its arrival to the heater's location where there is an abrupt change in the surface heat flux. The application of this phenomenon to a moving wall with frictional heating at its surface and to classical heat transfer in ducts can lead to new information. (C) 2008 Elsevier Ltd. All rights reserved.