The ignition of a solid exposed to a step in surface temperature, including the effect of the curvature, is analyzed by means of large activation energy asymptotics in the whole range of values of the Damköhler number,Da, which lead to a thermal runaway. For very large values ofDathe chemical reaction takes place in a surface boundary layer. The evolution of the temperature in this layer is described by a universal problem. Its solution contains a mathematical singularity, which identifies the ignition event occuring at an ignition time much smaller than the conduction time through the solid. WhenDais large but of the same order that the square of the nondimensional activation energy, the ignition time becomes of the order of the conduction time. The structure of the ignition problem is identical to that in the previous case, but its solution depends on the body size and shape. In both cases an initial quasisteady stage is followed by a transition stage in which the nonsteady effects must be retained. Finally, forDaof order unity the chemical reaction extends over the whole solid, and the ignition process can be described in terms of a first inert heating stage and a second reacting stage in which the temperature evolves according a nonsteady Frank-Kamenetskii equation.