The problem of a thermal explosion in the cylinder has been solved taking into account the natural convection. Both the classical solution of the Frank-Kamenetskii model and a realistic model of a thermal emission which takes into consideration reverse endothermic processes have been considered. It is shown that in this case the solution exists for any value of the energy influx into system. However, under certain conditions a sharp transition into the area of high temperatures still occurs which corresponds to the thermal explosion. It is shown that convection leads to significant change of the parameters of the thermal explosion. The results of this consideration are of interest for the theory of lasers and discharges where the Rayleigh numbers are rather large and the influence of convection appears to be essential. (C) 2007 Elsevier Ltd. All rights reserved.