A numerical investigation is made of natural convection of an incompressible fluid in a square cavity having a constant-temperature cold sidewall and an opposite hot sidewall with sinusoidally-varying temperature. Comprehensive numerical solutions to the Navier-Stokes equations are acquired for a fixed Rayleigh number and a Prandtl number, Ra = 10(7) and Pr = 0.7. The amplitude and frequency of the hot wall temperature oscillation are varied. The lime-mean heat transfer in the interior as well as the amplifications of fluctuations of instantaneous heat transfer are analyzed. The results disclose that a large-amplitude wall temperature oscillation causes an augmentation of the time-mean heat transfer rate. The maximum gain of the time-mean Nusselt number in the interior occurs at the resonance frequency, at which maximal fluctuations of the Nusselt number are found. The mechanism for resonant enhancement of the time-mean heat transfer is described. (C) 1998 Elsevier Science Ltd. All rights reserved.