Experiments have given evidence of strong sensitivity of the stagnation-point heat transfer on cylinders to small changes in the intensity of free-stream turbulence. A similar effect on local heat-transfer rates to flat plates has been measured, but only when a favourable pressure gradient is present. In this work it is theorized that vorticity amplification by stretching is a possible, and perhaps the dominant, underlying mechanism responsible for this sensitivity. A mathematical model is presented for a steady, basically plane stagnation flow into which is steadily transported disturbed unidirectional vorticity having the only orientation susceptible to stretching. The resulting velocity and temperature fields in the stagnation-point boundary layer are analysed assuming the fluid to be incompressible and to have constant properties. By means of iterative procedures and electronic analogue computation an approximate solution to the full Navier-Stokes equations is achieved which indicates that amplification by stretching of vorticity of sufficiently large scale can occur. Such vorticity, present in the oncoming flow with a small intensity, can appear near the boundary layer with an amplified intensity and induce substantial three-dimensional effects therein. It is found that the thermal boundary layer is much more sensitive to the induced effects than the velocity boundary layer. Computations indicate that a certain amount of distributed vorticity in the oncoming flow causes the shear stress at the wall to increase by 5%, while the heat transfer there is augmented by 26% in a fluid with a Prandtl number of 0.74. Preliminary computations reveal that the sensitivity of the thermal boundary layer increases with Prandtl number.