The unsteady forced convection involved in incompressible laminar boundary-layer over a semi-infinite plate is investigated. Initially, a steady state convective heat transfer with constant plate temperature or constant plate heat flux is established between the plate and the flow. By differential method, we study the thermal effect on this first state of a positive or a negative sudden change in either the plate temperature or plate heat flux. Numerical solution of differential equations is obtained for the whole transient from the initial steady state to the final one. Detailed results of the effect of the wall conditions change on the transient process are given for the fluids encountered in the usual applications (0.6 ≤ Pr ≤ 100). An exponential law of the instantaneous heat coefficient is deduced as function of Pr in the said Prandtl number range.