For exothermic reactions obeying the Arrhenius equation the critical conditions for thermal ignition are known to exist for activation energy E large enough satisfying ϵ ≡ RT a E < ϵ tr . This transition value ϵ tr of ϵ has values less than 0.25 in all geometries, (Boddington et al. [1]) and exactly 0.25 for the uniform temperature reactor (the Semenov case). The precise values of α tr and the corresponding values of the maximum dimensionless temperature θ and the Frank-Kamenetskii parameter δ (the transition values) were calculated for a slab by Boddington et al. [2] and Kordylewski [3] for infinite Biot number (Frank-Kamenetskii conditions). Kordylewski [3] gave a precise criterion for the appearance of these transition conditions and calculated the transition values for the other class A geometries of an infinite circular cylinder and a sphere, also for infinite Biot number. This criterion is modified here to the case of finite Biot number to obtain the transition values for a range of Biot numbers. The transition values are shown to match on to the values of the Semenov case for small values of the Biot number α as ϵ tr= 0.25 − O(α 2), ϵ tr= 4(j + 1)α/e 2) +O(α 2), θ tr= 4 + O(α), where j = 0, 1, 2 for slab, cylinder, and sphere, respectively.