The thermal ignition of a reacting boundary-layer flow over the hot surface of a wedge/ cone with an unheated starting length, L, is studied analytically and numerically. For the realistic situation of large activation energy reactions, a locally similar solution is derived and is found to agree well with the numerical solution within a wide range of L, geometric angle and the Prandtl number, Pr. An increase in L is shown to reduce the minimum ignition distance, because the flow velocity is reduced by the viscous drag over the starting length so that the flow over the heated section is heated to a greater extent for the same distance.