The heat flow on a cylinder immersed in an infinite rarefied gas is well defined in the free molecular limit. To first order in the inverse Knudsen number, the correction to this free molecular value diverges logarithmically, for a reason quite similar to that explaining the divergence of the virial expansion of transport coefficients of two−dimensional gases. When one accounts for the most divergent terms of an expansion of this flux in powers of the inverse Knudsen number, this logarithmic divergence does not disappear, due to hydrodynamical phenomena taking place at a distance from the cylinder that is much larger than the mean free path. This situation is somewhat similar to that encountered in studying the divergent transport coefficients of two−dimensional gases. It is discussed from the point of view of a possible experiment.