Experimental heat transfer data are presented for a series of asymptotic accelerated turbulent boundary layers for the case of an impermeable wall, and several cases of blowing, and suction. The data are presented as Stanton number versus enthalpy thickness Reynolds number. As noted by previous investigators, acceleration causes a depression in Stanton number when the wall is impermeable. Suction increases this effect, while blowing suppresses it. The combination of mild acceleration and strong blowing results in Stanton numbers which lie above the correlation for the same blowing but no acceleration. Velocity and temperature profiles are presented, from which it is possible to deduce explanations for the observed behavior of the Stanton number. A prediction scheme is proposed which is demonstrated to quite adequately reproduce the Stanton number results, using correlations derived from the profiles.