The transient stage of evolution in size, temperature and composition of a droplet, which nonisothermaly condenses or evaporates in the diffusion or free-molecular regime in the atmosphere of two condensable vapors and neutral carrier gas, is considered. On this stage, both solution concentration and temperature in the droplet approach their stationary values, and the steady rate of the droplet growth or evaporation establishes. The fact that the temperature adjusts fast to the current value of solution concentration in the droplet allows us to express the current solution concentration as an analytical function of temperature and to find general integral relations expressing the droplet radius and time as nonlinear functions of current droplet temperature. Some numerical illustrations of the theory have been done in the situation when the droplet size changes in the diffusion regime and the solution in the droplet can be considered ideal. In order to cover arbitrary initial droplet size and component concent