We determine the reaction progress function for an ideal hot spot model problem. The considered problem has an exact analytic solution that can be derived from a reduction of A. Nichols’ statistical hot spot model [1]. We perform numerical calculations to verify the analytic solution and to illustrate the error realized in real, finite systems. We show how the baseline problem, which does not distinguish between the reactant and product densities, can be scaled to handle general cases for which the two densities differ.