Methods, apparatus, and articles of manufacture control a device or system that has an operational limit related to the rate or frequency of operation. The frequency of operation is controlled at a variable rate calculated to maximize the system or apparatus performance over a calculated period of time short enough that a controlling factor, such as power consumption, does not vary significantly during the period. Known system parameters, such as thermal resistance and capacitance of an integrated circuit (IC) and its package, and measured values, such as current junction temperature in an IC, are used to calculate a time-dependent frequency of operation for the upcoming time period that results in the best overall performance without exceeding the operational limit, such as the junction temperature.