By assuming simple initial conditions for a surface-renewal calculation of thermal coupling between a thick solid and a well-mixed, low-Prandtl-number fluid, it has been possible to approximate the temperature variance near the wall in terms of a straightforward quadrature. Comparisons have been made with several experiments. The results are aimed at numerical solutions of the turbulent variance transport equation, which has thus far been solved with ad-hoc boundary conditions applied at solid walls.

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