<p>The paper presents the results of numerical simulation of heat exchange during cooling of a heated metal cylinder by a laminar gas–liquid flow in a vertical annular channel. The results were obtained based on a mathematical model of conjugate heat exchange between a gas–liquid flow and a metal cylinder in a two-dimensional nonstationary formulation that takes into account the axisymmetry of the ascending flow of the cooling medium relative to the longitudinal axis of the cylinder. The control volume method was used to solve the system of differential equations. The flow field parameters were calculated using the SIMPLE algorithm. The Gauss–Seidel method with lower relaxation was used for the iterative solution of systems of linear algebraic equations. The heat exchange parameters were obtained for cooling a high-temperature metal cylinder by a gas–liquid flow taking into account vaporization. The dynamics of changes in the structural-phase transformations of the cylinder material depending on the cooling rate is analyzed.</p>