  We report a new thermal boundary layer equation for turbulent Rayleigh-Benard
convection for Prandtl number Pr>1 that takes into account the effect of
turbulent fluctuations. These fluctuations are neglected in existing equations,
which are based on steady-state and laminar assumptions. Using this new
equation, we derive analytically the mean temperature profiles in two limits:
(a) Pr>1, Pr~1 and (b) Pr>>1. These two theoretical predictions are in
excellent agreement with the results of our direct numerical simulations for
Pr=4.38 (water) and Pr=2547.9 (glycerol) respectively.
