We carry out the linear viscous-irrotational analysis of capillary instability with heat transfer and phase change. We consider the cylindrical interface shared by two viscous incompressible fluids enclosed by two concentric cylinders. In viscous potential flow, viscosity enters the model through the balance of normal stresses at the interface. We write the dispersion relation from the stability analysis for axisymmetric disturbances in terms of a set of dimensionless numbers that arise in this phase change problem. For the film boiling condition, plots depicting the effect of some of these parameters on the maximum growth rate for unstable perturbations and critical wavenumber for marginal stability are presented and interpreted. Viscous effects of a purely irrotational motion in the presence of heat and mass transfer can stabilize an otherwise unstable gas-liquid interface.