In an embodiment, a processor comprises: a plurality of cores each to execute instructions; a plurality of thermal sensors, at least one of which is associated with each of the cores; and a power control unit (PCU) coupled to the cores. The PCU includes a thermal control logic to preemptively throttle a first core by a first throttle amount when a temperature of a second core exceeds at least one thermal threshold. Note that this first core may be preemptively throttled independently of a throttling of the second core and may have a temperature of the first core does not exceed any thermal threshold. Other embodiments are described and claimed.