This paper presents a Lattice Boltzmann (LB) model for incompressible axisymmetric thermal flows. The forces and source terms are added into the Lattice Boltzmann Equation (LBE) and the incompressible Navier-Stokes equations are recovered by the Chapman-Enskog expansion. The model of Zhou [1] is applied for axial, radial and azimuthal velocities and the model of Q.Li et al [2] is computed for temperature variation. The source term of the scheme is simple and without velocity gradient terms. This approach can solve problems including several physical phenomena and complicated force forms as the flow between two coaxial cylinders. Good agreement is obtained between the present work, the analytic solutions and results of previous studies in cylindrical pipe. It proves the efficiency and simplicity of the proposed model compared to other ones. The Taylor-Couette (TC) system is treated with water flow characterized by a radius ratio η = 0.5 and an aspect ratio Γ = 3.8. Three Reynolds numbers of 85, 100 and 150 are tested. The influence of the end-wall boundary conditions and the influence of thermal conditions on the flow structure and on the temperature distribution along the inner and outer cylinders are analyzed.