The free surface behaviour of a volatile wetting liquid at low gravity is studied using scaling and numerical techniques. An open cavity model, which was applied in part 1 to investigate fluid flow and heat transfer in non-deforming pores, is used to evaluate the influence of convection on surface morphology with length scales and subcooling/superheating limits of 1 ≤ D ≤ 102 μm and ∼ 1 K, respectively. Results show that the menisci shapes of highly wetting fluids are sensitive to thermocapillary flow and to a lesser extent the recoil force associated with evaporation and condensation. With subcooling, thermocapillarity produces a suction about the pore centreline that promotes loss of mechanical equilibrium, while condensation exerts an opposing force that under some conditions offsets this destabilizing influence. With superheating, thermocapillarity and evaporation act in the same direction and mutually foster surface stability. All of these trends are magnified by high capillary and Biot numbers, and the stronger circulation intensities associated with small contact angles. These phenomena strongly depend on the thermal and interfacial equilibrium between the liquid and vapour, and have important ramifications for systems designed to maintain a pressure differential across a porous surface.