The issue of hydromagnetic instability for a viscoelastic condensate film streaming down on a normal moving cylinder is discussed. As the visco-elasticity, heat-transfer influence or the magnetic field are included into the governing equations, the results become more suitable with the real situation. The nonlinearity enhances the accuracy of the results. The flow stability is weakened by the reduction of the volume of cylinder. However, the response of the system due to the temperature difference is uncertain. Moreover, the increment of magnetic field can enhance the stability. In contrast to the linear-results, the flow can be stabilized by the rheology.