(Currently Amended) A method of stretch-forming a metal workpiece, comprising: providing a heat-insulating enclosure that includes first and second aligned and opposed workpiece openings (50A and 56A) in respective first and second spaced-apart sidewalls (44A and 44B) of the enclosure between which a die with a working face having a predetermined cross-sectional profile is positioned to receive the workpiece, wherein at least the working face comprises a thermally insulated material; providing first and second opposed jaws (22A and 22B) mounted on respective first and second opposed swing arms (16A and 16B); providing a heater (26 or 64) for electric resistance heating the workpiece to a working temperature; providing a radiant heater (49A, 49B, 72A-72F, and 74A-74F) for applying radiant heat to one or more predetermined portions of the workpiece to increase the plastic elongation of the workpiece at the one or more predetermined portions; positioning the workpiece in the enclosure in forming proximity to the working face of the die with its opposite ends extending through respective ones of the first and second openings (50A and 56A) in sidewalls (44A and 44B) of the enclosure; electrically insulating the workpiece; gripping the workpiece in the jaws (22A and 22B) at its opposite ends; resistance heating the workpiece to a working temperature by passing electrical current through the workpiece; moving the workpiece and the working face of the die relative to each other while the workpiece is at the working temperature, thereby forming the workpiece against the working face of the die into a preselected form; at one or more predetermined positions of the workpiece in relation to the die, applying radiant heat to one or more predetermined portions of the workpiece to increase the plastic elongation of the workpiece at the one or more predetermined portions; and cooling the workpiece while the workpiece is in the preselected form against the working face of the die. providing a heat-insulating enclosure that includes first and second aligned and opposed workpiece openings (50A and 56A) in respective first and second spaced-apart sidewalls (44A and 44B) of the enclosure between which a die with a working face having a predetermined cross-sectional profile is positioned to receive the workpiece, wherein at least the working face comprises a thermally insulated material; providing first and second opposed jaws (22A and 22B) mounted on respective first and second opposed swing arms (16A and 16B); providing a heater (26 or 64) for electric resistance heating the workpiece to a working temperature; providing a radiant heater (49A, 49B, 72A-72F, and 74A-74F) for applying radiant heat to one or more predetermined portions of the workpiece to increase the plastic elongation of the workpiece at the one or more predetermined portions; positioning the workpiece in the enclosure in forming proximity to the working face of the die with its opposite ends extending through respective ones of the first and second openings (50A and 56A) in sidewalls (44A and 44B) of the enclosure; electrically insulating the workpiece; gripping the workpiece in the jaws (22A and 22B) at its opposite ends; resistance heating the workpiece to a working temperature by passing electrical current through the workpiece; moving the workpiece and the working face of the die relative to each other while the workpiece is at the working temperature, thereby forming the workpiece against the working face of the die into a preselected form; at one or more predetermined positions of the workpiece in relation to the die, applying radiant heat to one or more predetermined portions of the workpiece to increase the plastic elongation of the workpiece at the one or more predetermined portions; and cooling the workpiece while the workpiece is in the preselected form against the working face of the die.