In this paper, a new immersed boundary-lattice Boltzmann method (IB-LBM) is developed to simulate heat transfer problems with constant heat flux boundary condition. In this method, the no-slip boundary condition is enforced via implicit velocity correction method and the constant heat flux boundary condition is implied considering the difference between the desired heat flux and the estimated one. The velocity correction represented as a forcing term is added to Boltzmann equation and for temperature correction, a heat source/sink term is introduced to energy equation. Elimination of sophisticated grid generation process, simplicity and effectiveness while keeping the accuracy, are the main advantages of the proposed method. Using the developed method, natural convection around a hot circular cylinder with constant heat flux in an enclosure with cold walls has been simulated at Rayleigh numbers of 103–106. Moreover, effects of diagonal position of cylinder on the flow and heat transfer patterns and local Nusselt number distribution on the surface of cylinder and walls of enclosure have been investigated. The obtained results show that the location of maximum local Nusset number is extremely depended on the diagonal position of the cylinder. According to the results of this simulation, it can be said that the present method is able to imply accurately the constant heat flux boundary condition.