This report presents the results of experimental and theoretical research of aerodynamics and convective heat transfer in cyclone devices with the new system of external recirculation of heating gas under the influence of radial pressure gradient in a heat carrier’s swirling turbulent flow. The dynamic problem of tangential velocity distribution in a clearance volume is solved at various re-circulation ratio values including limiting quantities (kr = 0; 1) and variations in cyclonic combustion chamber’s design parameters and operating conditions (Rer); the integrated calculation ratios for fundamental aerodynamic characteristics of a recirculation device are derived. The first experimental and numerical studies of convective heat transfer on internal and external surfaces of a hollow shaft in a swirling recirculation flow are derived through the instrumentality of OpenFOAM, these studies are also conducted for a setting of several cylindrical solid inserts. The external surface heat problem of a hollow cylindrical insert is solved with integral and digital methods; generalized similarity equations for the internal and external surfaces extended in range of Reynolds number are derived. The experimental data is in reasonable agreement with the derived curves and the results of mathematic modelling of convective heat transfer. Calculation recommendations for optimal selection of kr values at various ratios of their geometric characteristics and products utilization rate are obtained.