The variations of root-mean-square (r.m.s.) temperature and velocity in turbulent thermal convection above a heated, horizontal surface are analyzed by extending the arguments of Castaing ei al. ([1] : J. Fluid Mech. 204, 1-30 (1989)) which lead to the two-sevenths power law for heat transfer. Asymptotic matching of properties scaled on Deardoff’s convection scales with those scaled on Castaing et al.’s lambda-layer show that the r.m.s. temperature decays as z(-1/2) and the r.m.s. vertical velocity increases as log z. These results are supported by data from Rayleigh convection and unsteady convection,both penetrative and non-penetrative.