1. A processor comprising: at least one lower processing capability and lower power consumption physical compute element; at least one higher processing capability and higher power consumption physical compute element; migration performance benefit evaluation logic of the processor to evaluate a performance benefit of a migration of a workload from the at least one lower processing capability and lower power consumption physical compute element to the at least one higher processing capability and higher power consumption physical compute element, and to determine whether or not to allow the migration based on the evaluated performance benefit; available energy and thermal budget evaluation logic of the processor to evaluate available energy and thermal budgets of the processor and to determine to allow the migration if the migration fits within the available energy and thermal budgets or not allow the migration if the migration does not fit within the available energy and thermal budgets; and workload migration logic of the processor to perform the migration of the workload when allowed by both the migration performance benefit evaluation logic and the available energy and thermal budget evaluation logic.