Abstract: In this paper, the thermal lattice Boltzmannscheme has been improved, which was proposed by J. G. M. Eggels and J. A.Somers, and a new equilibrium solution for temperature distribution functionhas been presented on the incompressible flow assumption. This newequilibrium solution can correct the compressibility effect on macroscopictemperature, and modify the statistical definition of macroscopictemperature. The half-way bounce-back boundary condition was used in themethod proposed by J. G. M. Eggels and J. A. Somers for velocity andtemperature. However, the boundary condition was not accurate for thetemperature in the physical view. Therefore, a non-equilibrium extrapolationscheme, which is a simple algorithm and very easy to implement, has beenadopted for velocity and temperature in the boundaries. Subsequently, theimproved TLBM has been used to simulate the natural convection in the cavityat Ra=10^6 and Pr=0.71 for air. The flow parameters obtained in thesimulation agreed very well with those of other numerical methods, toindicate that the improved TLBM can be used to simulate the non-isothermalflows efficiently and accurately.