An iterative direct-forcing immersed boundary method is extended and used to solve convection heat transfer problems. The pressure, momentum source, and heat source at immersed boundary points are calculated simultaneously to achieve the best coupling. Solutions of convection heat transfer problems with both Dirichlet and Neumann boundary conditions are presented. Two approaches for the implementation of Neumann boundary condition, i.e. direct and indirect methods, are introduced and compared in terms of accuracy and computational efficiency. Validation test cases include forced convection on a heated cylinder in an unbounded flow field and mixed convection around a circular body in a lid-driven cavity. Furthermore, the proposed method is applied to study the mixed convection around a heated rotating cylinder in a square enclosure with both iso-heat flux and iso-thermal boundary conditions. Computational results show that the order of accuracy of the indirect method is less than the direct method. However, the indirect method takes less computational time both in terms of the implementation of the boundary condition and the post processing time required to compute the heat transfer variables such as the Nusselt number. It is concluded that the iterative direct-forcing immersed boundary method is a powerful technique for the solution of convection heat transfer problems with stationary/moving boundaries and various boundary conditions.