In this paper, heat conduction coupled with multiphase changes are considered in a cylindrical multilayer composite accounting for thermal contact resistance depending on contact pressures and roughness parameters. A numerical simulation is proposed using both analytical developments and numerical computations. The presented modeling strategy relies on an algorithm that alternates between heat conduction accounting for volumetric heat sources and a multi-phase change model based on non-isothermal Avrami's equation using the isokinetic assumption. Applications to coiling process (winding of a steel strip on itself) are considered. Indeed, phase changes determine the microstructure of the final material and are responsible for residual stresses that create flatness defects. A Finite Element modeling is used for validating the presented solution and numerical results are presented and discussed.