A complete system of Navier-Stokes equations is considered, the solutions of which describe the motion of a viscous heat-conducting gas. The paper presents an approximate analytical approach for representing solutions of the Navier-Stokes equations describing one-dimensional unsteady flows arising in the problem of thermal interaction between a flow of a gas at rest and a heatconducting stationary wall, the initial temperature of which differs from the initial temperature of the gas. In the framework of the conjugate approach, the solution of the problem is complicated by the need to jointly solve the differential equations for gaseous medium and wall material. As a result of unsteady gas-wall interaction, gasdynamic and thermal processes cause the appearance of a flow with complex internal structure. In order to describe the emerging flow, taking into account the influence of dissipative effects, leads to the need to use the complete system of nonlinear differential Navier-Stokes equations in partial derivatives, which are based on the universal laws of conservation of mass, momentum and energy, and constitute a theoretical basis for describing and predicting a wide range of phenomena in gas dynamics [1, 2]. The temperature distribution inside the wall is modeled by a linear equation of heat conduction. At moderate differences in gas-wall initial temperatures, perturbations of the parameters are small, and the flow field is studied based on the solution of a system of the Navier-Stokes equations, linearized around the initial state. Structure of the emerging flows is studied on the basis of the joint solution of a linearized system of the Navier-Stokes equations and the equation of heat conduction of the wall for given initial and boundary conditions[2]. Analytical solutions of the linearized problem and asymptotic expressions for gas-wall parameters, that describe formation of the continuous structure of the flow field and distribution of the wall temperature, are obtained by the Laplace transform method. These solutions make it possible to study the influence of viscosity, heat conduction and other physical factors on formation of dissipative and ideal nonviscous and non-heat-conducting zones in gas flow field. It should be noted that linearized solutions, describing the continuous structure of the emerging flow, are also of interest as a test in the development and debugging of algorithms for numerical solution of the Navier-Stokes nonlinear equations. This work is supported by the National Agency for Research and Development under the grant No. 20.80009.5007.13.