The stabilization of thermal runaway in nearly ignited plasmas by actively controlled auxiliary heating is considered. The use of a variable amount of auxiliary heating for burn control can greatly increase the values of the power multiplication factor Q (fusion power/auxiliary heating power) relative to those values permitted with constant auxiliary heating. A one-dimensional calculation is used to determine the maximum allowable deviation from thermal equilibrium as a function of the equilibrium temperature and Q. The results are applied to tokamak plasmas. The effect of the auxiliary heating deposition profile upon Q is determined. For fixed deviation from thermal equilibrium, significantly higher values of Q can be obtained with central ion heating relative to those obtained with edge ion heating. Central electron heating has about the same order of effectiveness as edge ion heating. For central temperatures of ∼ 25 keV, Q ∼ 25 can be obtained if the deviation in the ion temperature is held below 15%.