Current approximation methods for space-time reactor problems with temperature feedback lack an error estimate. The method discussed in this paper yields an approximate solution with an error estimate. Upper and lower bounds are sought for the flux and temperature at all points in a reactor for all time. The bounds are the solutions of a set of ordinary differential equations which are similar to the point model equations. Having chosen an unusual nonlinear form for the bounds, a comparison theorem of the Nagumo-Westphal type is used to derive the equation which the bound must satisfy. Optimum control theory and Pontryagin’s Maximum Principle determine the optimum bounds.In an example, bounds are determined for three standard nonlinear reactor models. The bounds are narrow and lead to interesting conjectures about the exact solution.