Stanton number measurements are presented for the turbulent boundary layer flow of air on rough-wall flat plates with both constant wall temperature and step wall temperature boundary conditions. Two rough surfaces were used—one roughened with hemispheres spaced four diameters apart and the other with hemispheres spaced two diameters apart. The data are compared with each other and with results from a smooth surface tested in the same experimental facility. It is found that, when plotted as the ratio of Stanton number to constant wall temperature Stanton number vs the ratio of unheated length to distance from the leading edge, the data from the smooth and rough surfaces scatter about a single curve. This gives a new kernel function that, when used in the superposition solution of the arbitrary wall temperature problem, yields good results for both smooth and rough surfaces.