Abstract <p>The results of numerical 3D modeling of freely convective heat-exchange processes in the channels of one of the main variants of a panel-radiant room-heating system with a ribbon finning system have been presented. The spatial distributions of the thermophysical parameters of free-convective air flows have been determined both in the internal and external regions of the system in wide ranges of changes in the basic operating and geometric parameters of the BS. The features of the behavior of the heat-transfer coefficients from the BS heating surfaces to the updraft have been calculated and established. The criterion dependences for calculating the Nusselt numbers on the modified Rayleigh number and other parameters of the vertical channels of the baseboard system have been proposed. A formula for calculating the specific heat removal capacity from the heating surfaces of the system’s internal elements has been obtained. It has been shown that the specific heat-removal capacity nonmonotonously depends on the ratio of the lengths of intercostal gaps in adjacent channels, at certain values of which there is an extremum. The relations between the capacities of convective and radiative heat fluxes generated in the considered heat-exchange system have been established. Recommendations on the choice of basic geometric and operating parameters that can provide an increase in heat removal by 20–30% compared to the practical BSs with a belt finning system have been given.</p>