Abstract: This paper proposes a method of analysis for problems of complex heat transfer in high-temperature furnaces, based upon the idea of thermal resistances in series and in parallel, and gives formulae for calculating the chief items of thermal resistances in a rotary kiln. It is proposed to use △(Tn) as the driving force in radiant heat-transfer. In a full discussion of periodic heat-flow into and from a refractory lining, it is pointed out that the "Thermal impedance" applicable to average values of temperature and heat flow is different from the ordinary a.c. impedance (applicable to r.m.s. values), and an approximate formula based upon rational analysis is given. The simplified mechanism of heat transfer between granules of calcinated material is also discussed.