The article discusses the process of heat exchange of a finned wall with a coolant. The temperature field in the wall volume was determined on the basis of a numerical solution of the two-dimensional heat conduction problem, and the analysis of the characteristics of temperature distributions was carried out according to the simulation results. The values ​​of the heat transfer coefficient of cooling fins of rectangular section are calculated for two variants of heat transfer conditions at the end of the fins in a wide range of dimensionless parameters. The error in calculating the heat transfer coefficient in the approximation of a thin rib is determined using a one-dimensional computational model.