As non-body conforming numerical methods using simple Cartesian mesh, immersed boundary methods have become increasingly popular in modeling fluid-solid interaction. They usually do this by adding a body force term in the momentum equation. The magnitude and direction of this body force ensure that the boundary condition on the solid-fluid interface is satisfied without invoking complicated body-conforming numerical methods to impose the boundary condition. A similar path has been followed to model forced convection heat transfer by adding a source term in the energy equation. The added source term will ensure that thermal boundary conditions on the solid-fluid interface are imposed without invoking a boundary conforming mesh. These approaches were developed to handle the Dirichlet boundary condition (constant wall temperature). Few of them deal with the Neumann boundary condition (constant wall heat flux). This paper presents a simple new immersed boundary method. It can deal with the Dirichlet boundary condition, Neumann boundary condition and conjugated heat transfer by adding an energy source or sink term in the energy conservation equation. The presented approach is validated against the analytical solutions and a very good match is achieved.