High thermal transfer, hollow core extrusion screws (50, 52, 124, 126, 190) include elongated hollow core shafts (54, 128, 130, 192) equipped with helical fighting (56, 132, 134, 194) along the lengths thereof. The fighting (132, 134, 194) may also be of hollow construction which communicates with the hollow core shafts (54, 128, 130, 192). Structure (88, 90) is provided for delivery of heat exchange media (e.g., steam) into the hollow core shafts (54, 128, 130, 192) and the hollow fighting (132, 134, 194). The fighting (56, 132, 134, 194) also includes a forward, reverse pitch section (64, 162, 216). The extrusion screws (50, 52, 124, 126, 190) are designed to be used as complemental pairs as a part of twin screw processing devices (20), and are designed to impart high levels of thermal energy into materials being processed in the devices (20), without adding additional moisture.