In this study, the hybrid Lattice Boltzmann - Finite difference - Immersed Boundary method has been used for investigation of problems with heat transfer. For this purpose, mass and momentum conservation equations are solved by the Immersed Boundary- Lattice Boltzmann method and finite difference method has been used for solving energy conservation equation. The effect of Immersed Boundary has been shown as force and external energy source term in equations and therefor flow and heat transfer around circular cylinder and also the effect of how to move cylinder in heating of fluid inside the cavity has been studied. for this purpose four kinds of movements: circular reciprocating, normal circular, diagonal amplitude and horizontal amplitude have been considered for the cylinder and in all cases, the changes of force coefficients and Nusselt number have been discussed. It has been showed that the circular reciprocating movement has more effect on heating of fluid inside the cavity, which indeed this movement reduces the time of fluid heating about 20 percent in comparison with normal circular and diagonal amplitude movement and approximately 37 percent in comparison with horizontal amplitude movement. In all of the studied problems, the efficiency of hybrid method has been proved.