We consider the dynamics of multi-component heat-conducting viscous incompressible flow in a plane domain when the viscosity and thermal conductivity of the medium depend on temperature. The dynamics of the flow is governed by an initial-boundary value problem for the Navier–Stokes system with heat conduction and heat transfer taken into account. The existence of a generalized global solution with velocity field and temperature of Hopf's class has been established in conjunction with the estimate of fractional smoothness of the order 1/2 in the time variable.