The present study deals with unsteady laminar boundary layers in the immediate vicinity of the stagnation point of a heated blunt-nosed cylinder in an incompressible flow with unsteady velocity. An exact solution is presented for the special case of a flow velocity varying inversely with a linear function of time, together with calculated boundary-layer characteristics for different values of a flow parameter. Based on the results of this exact solution, an approximate method of solutions is proposed for a more general problem where the flow velocity changes arbitrarily with time. The results of five examples are shown and discussed in the light of other available solutions. Finally, the limitation of this approximate solution is pointed out and a possible remedy indicated.