A theoretical analysis of the distortion of unsteady three-dimensional disturbances in a Hiemenz boundary layer and its effect on the heat transfer enhancement is presented. It is shown that the disturbance length scale is a critical parameter in determining the amplification ratio of the incoming vorticity. For large disturbance length scales, the amplification ratio increases when the length scale decreases, and a maximum value occurs at a length scale close to five times the boundary-layer thickness. The unsteadiness of the disturbances is found to reduce the vorticity amplification, but the effect is second order when the frequency is low compared to the mean flow strain rate. The impinging disturbances induce large-amplitude vorticity of opposite sign at the wall whose magnitude controls the heat transfer enhancement. As an application of the present analysis, a new scaling correlation is derived for stagnation-point heat transfer in the presence of free-stream turbulence. The theoretical correlation, expressed in terms of turbulence intensity, integral length scale and mean flow Reynolds number, agrees reasonably well with recent experimental data.