For stationary, one-dimensional heat conduction in a gas at rest the Grad theory of 13-moments provides explicit differential equations for temperature. pressure tensor, and heat flux. In the planar case, where the fields depend only on one Cartesian coordinate, the heat flux is proportional to the temperature gradient, just as postulated by Fourier's law. However, this is no longer so in cylindrically or spherically symmetric problems with a radial heat flux. These latter cases are described here. It turns out that, while the pressure is still constant, - as in the planar case, - the pressure deviator does not vanish, in contrast to the Navier-Stokes theory. And the non-zero deviatoric pressure affects the relation between heat flux and temperature gradient so that Fourier's law is no longer valid. Consequently in a rarefied gas the temperature field is strongly affected by the new terms in the neighborhood of the cylinder axis or in the neighborhood of the center of the sphere. (C) 2004 Elsevier B.V. All rights reserved.