  This paper presents a mathematically exact self-similar solution to the joint
nonsteady problems of vapour diffusion towards a droplet growing in a
vapour-gas medium and of removal of heat released by a droplet into a
vapour-gas medium during vapour condensation. An equation for the temperature
of the droplet is obtained; and it is only at that temperature that the
self-similar solution exists. This equation requires the constancy of the
droplet temperature and even defines it unambiguously throughout the whole
period of the droplet growth. In the case of strong display of heat effects,
when the droplet growth rate decreases significantly, the equation for the
temperature of the droplet is solved analytically. It is shown that the
obtained temperature fully coincides with the one that settles in the droplet
simultaneously with the settlement of its diffusion regime of growth. At the
obtained temperature of the droplet the interrelated nonsteady vapour
concentration and temperature profiles of the vapour-gas medium around the
droplet are expressed in terms of initial (prior to the nucleation of the
droplet) parameters of the vapour-gas medium. The same parameters are used to
formulate the law in accordance with which the droplet is growing in diffusion
regime, and also to define the time that passes after the nucleation of the
droplet till the settlement of diffusion regime of droplet growth, when the
squared radius of the droplet becomes proportionate to time. For the sake of
completeness the case of weak display of heat effects is been studied.
