1. A multi-core processor computer system for conserving average operating power, comprising: a plurality of computer hardware processor cores that differ amongst themselves in at least in their respective operating power requirements and processing capabilities; a monitor for gathering performance and power metric information from each of said computer hardware processor cores that is specific to a particular run of application software then executing on a first computer hardware processor core in the plurality of computer hardware processor cores; and a workload transfer and control mechanism connected to the plurality of computer hardware processor cores and to the monitor, and providing for a transfer of said application software then executing to a second computer hardware processor core in the plurality of computer hardware processor cores.