Following the previous velocity-field study (Ishigaki 1970), this paper studies how the temperature field in the laminar boundary layer near a two-dimensional stagnation point responds to the main-stream oscillation. The time-mean temperature field is of particular interest and is studied in detail. The velocity field is treated as known and is taken from the previous paper. In § 3 the solutions over the whole frequency range are obtained under the assumption of small amplitude oscillation and the results are compared with the existing approximate solutions for low and high frequency in terms of heat transfer. Time-mean heat transfer decreases at low frequency, but slightly increases at high frequency. Two factors that cause time-mean modification of the temperature field are examined quantitatively. In § 4 the finite amplitude case is treated under the assumption of high-frequency oscillation and a few examples of the time-mean temperature profile are shown.