In an embodiment, a processor includes at least one execution unit to execute instructions, and an interrupt generation unit. The interrupt generation unit may be to: receive a plurality of values indicating thermal status values for a memory unit at multiple points in time across a first time window; determine a running average value based on the plurality of values indicating thermal status values in the memory unit; and in response to a determination that the running average value has exceeded a high thermal status threshold value, generate a thermal interrupt indicating a high thermal status event in the processor. Other embodiments are described and claimed.