A generalization of the method used in the kinetics of nonisothermal unary nucleation is proposed to construct the kinetic theory of nonisothermal binary nucleation allowing one to take account of the release of the latent heat of condensation. The three-dimensional balance equation describing the material and heat exchange of liquid solution particles with the surrounding vapor-gas medium is obtained. Independent variables in this equation are the numbers of molecules of each component in a liquid solution nucleus and its temperature. Going beyond the framework of the Fokker-Planck approximation is proposed for the corresponding kinetic equation. A hierarchy of time scales of nonisothermal binary nucleation is established and an analytical description of the thermal relaxation of the nuclei is given. Theoretical results are illustrated by numerical calculations for the nucleation in a water-ethanol system.