A combination of high space velocities, a very exothermic reaction, and an active catalyst gives rise to large temperature gradients, or hot spots, during the catalytic oxidation of CH4 to CO and H-2. These hot spots have been detected visually and with an optical pyrometer during the oxidation reaction over a Ni/Yb2O3 catalyst. The temperature of the hot spot may be as much as 300-degrees-C greater than the temperature measured by a thermocouple located only a short distance from it in the catalyst bed. If the lower temperature is used to calculate the equilibrium concentrations of CH4, CO, CO2, and H-2, it is possible to reach the conclusion that the concentrations of CO and H2 exceed their thermodynamic equilibrium values. But if the true maximum (hot spot) temperature is used, the observed concentrations are somewhat less than those predicted at equilibrium.