Abstract In handling the effects of longwave radiant exchange in an enclosure, it is useful to have two measures for the global temperature; the space or volume-averaged observable radiant temperature T rv , and the temperature T rs at the star point when the physical surface-to-surface pattern of radiant exchange is replaced by an approximately equivalent surface-to-star point pattern. T rv is needed in connection with our perception of thermal comfort, but is difficult to estimate: T rs is fictitious but is easy to calculate. It would be convenient if T rs could be used as a satisfactory estimate of T rv . This proves to be the case for enclosures which are not too far from cubic, but it is not true for all shapes. The case of radiant exchange in a triangular enclosure is also discussed since the transformation to a star pattern is exact.