A processor of an aspect includes at least one lower processing capability and lower power consumption physical compute element and at least one higher processing capability and higher power consumption physical compute element. Migration performance benefit evaluation logic is to evaluate a performance benefit of a migration of a workload from the at least one lower processing capability compute element to the at least one higher processing capability 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 is to evaluate available energy and thermal budgets and to determine to allow the migration if the migration fits within the available energy and thermal budgets. Workload migration logic is to perform the migration when allowed by both the migration performance benefit evaluation logic and the available energy and thermal budget evaluation logic.