Statistics of heat transfer in two-dimensional (2D) turbulent Rayleigh-Bénard (RB) convection for and are investigated using the lattice Boltzmann method (LBM). Our results reveal that the large scale circulation is gradually broken up into small scale structures plumes with the increase of , the large scale circulation disappears with increasing , and a great deal of smaller thermal plumes vertically rise and fall from the bottom to top walls. It is further indicated that vertical motion of various plumes gradually plays main role with increasing . In addition, our analysis also shows that the thermal dissipation is distributed mainly in the position of high temperature gradient, the thermal dissipation rate already increasingly plays a dominant position in the thermal transport, can have no effect with increase of . The kinematic viscosity dissipation rate and the thermal dissipation rate gradually decrease with increasing . The energy spectrum significantly decreases with the increase of . A scope of linear scaling arises in the second order velocity structure functions, the temperature structure function and mixed structure function(temperature-velocity). The value of linear scaling and the 2nd-order velocity decrease with increasing , which is qualitatively consistent with the theoretical predictions.