Prediction of heat and mass transfer during post nucleation growth of liquid microdroplets in a supersaturated mixture of vapor and non-condensable gas is difficult because in the early stages of the process, the droplet size is usually comparable to the mean free path of the surrounding gas molecules. Transport then falls in the transition regime between free molecular flow and continuum transport. In the study reported here, a direct simulation Monte Carlo (DSMC) scheme was used to model the molecular transport during quasi-equilibrium condensation growth of water microdroplets in supersaturated mixtures of water vapor and a non-condensable gas. A new treatment of the boundary conditions at the droplet interface is proposed which properly accounts for the energy and mass balance at the interface as well as thermodynamic requirements that must be imposed there. This treatment makes it possible to predict the initially unknown droplet interface temperature as part of the simulation calculation. Predictions of this scheme for water-argon mixtures are shown to agree closely with measured droplet growth rate data. Simulation results are also presented for mixtures of water vapor and nitrogen. The effects of varying droplet size and ambient concentration on transport are explored in detail for microdroplet condensation in the transition regime.