Models to express the responses of N and S mineralization to temperature are essential to predict the amounts of plant-available N and S released from soil organic matter. We improved the methods conventionally used to describe temperature dependence by fitting, simultaneously, kinetic models and temperature-response functions. Net N or S mineralization was defined as a function of temperature, time, and length of incubation interval. These single-step models facilitated objective comparisons of rival temperature functions. The various functions represented rival hypotheses about the temperature dependence of mineralization. Temperature responses traditionally have been described by Arrhenius or Q10 (temperature coefficient) functions, but a quadratic function was required to describe declining responses at warm temperatures. We compared the Arrhenius and Q10 functions, and showed how indices of temperature response (activation energy and Q10) are derived from the finite differentials of the response functions. Single values of Q10 described rates that climbed exponentially with temperature, but separate values of Q10 for each temperature interval (5-15, 15-25, and 25-30-degrees-C) were required when the responses diminished in warm soils (quadratic response). Temperature was a major factor influencing N and S mineralization in a sequence of soils under the following management regimes: native forest, recently cleared forest, and long-term cultivation. Various combinations of kinetic equations and temperature functions were required to describe the time and temperature dependence of mineralization in soils under contrasting management. The models were proposed as multiple working hypothesis about the processes involved in mineralization.