A typical temperature for the quiet solar corona is ~ 1.5 x 106K, whereas the photosphere – the likely source of the thermal energy – has a temperature less than 6 × 103 K. Although many theories have been advanced to explain why the corona is so much hotter than the photosphere, this old problem remains unsolved. However, there is a mechanism based on second-order transport that may provide the answer, or at least part of the answer. This process, described by the author in Thermodynamic inequalities in gases and magnetoplasmas, John Wiley & Sons Ltd, 1996, causes heat to be transported across strong magnetic fields up temperature gradients.