The heat and mass transfer in a porous wick within a capillary evaporator were analyzed in three dimensions, using a pore network model to simulate immiscible liquid–vapor flow and phase changes in the capillary structure. Characteristics of the porous structure, such as pore radius distribution, permeability and porosity were obtained from measurements of an actual wick and were included in the calculations. Scenarios involving both a fully liquid-saturated and an unsaturated wick containing liquid and vapor were examined under steady state conditions. The location at which the initial vapor phase was generated was identified based on classical nucleation theory. The transition from a saturated to an unsaturated wick was assessed by modeling the distribution of the liquid–vapor interface, and the wicks were compared based on color 3D renderings of temperature and pressure distributions and meniscus curvatures. The maximum temperature of the unsaturated wick exceeded that of the saturated wick although the area of the liquid–vapor interface in the unsaturated wick was five times that in the saturated wick. Since a distribution of pore radii was considered in these calculations, the interface within the wick was not smooth but exhibited asperity. The distribution of meniscus curvatures in the unsaturated wick was much wider compared with the saturated wick. The results obtained in the case of an unsaturated wick demonstrated the occurrence of the heat pipe effect, induced by a distribution of capillary pressures.