The partial differential equation for heat diffusion is numerically integrated by the Runge-Kutta method. Solutions are obtained for the diurnal temperature variation with a bounded coefficient of eddy diffusivity which varies periodically with time and exponentially with height. The surface wave is represented by the sum of a diurnal and a semidiurnal harmonic wave. The results may be interpreted to apply over a fairly broad range of diffusivity values and height. With appropriate choices of the various parameters, reasonably good agreement is obtained between theoretical and observational values of amplitude reduction and phase lag as functions of height and time.