Low Rayleigh number thermal convection in a fluid layer confined between two-infinite horizontal walls kept at spatially sinusoidal temperature distributions, T_L=T_m+Delta Tsin kappax,;T_U=T_m+Delta Tsin(kappax-eta)$, is theoretically investigated by a regular perturbation expansion method. For small wave numbers, an upright cell is formed between the two walls at $eta$=0. The cell is tilted, as the phase difference increases, and a flow with tow counter-rotating eddies occurs at $eta=pi$. when the wave number is large, isolated eddies are formed near the lower and upper walls, for all the phase differences. There exists a wave number at which maximum heat transfer rate at the walls occurs, at each of the phase differences. And the wave number increases with increase of the phase difference. for a fixed wave number, the heat transfer rate decrease with increase of the phase difference.