The simplified model for the warm-up of monolithic reactors under non-reacting conditions that has been proposed and solved numerically by Kollsakis (1997) is analysed from a mathematical point of view. For the case of zero wall conductivity a previously known analytical solution is discussed. A new analytical solution based on expansion in a series of non-orthonormal eigenfunctions is given for the case of finite conductivity. Also the Green functions of the problem are derived and their use is pointed out for tackling the problem with additional source terms or/and boundary conditions. General advice is given for the choice of the best solution method depending on the values of the problem parameters.