An apparatus and method for forming a composite workpiece are provided. An electromagnetic field generator induces a current in a susceptor, thereby heating the workpiece in a die cavity. An elastomeric bladder in the cavity is inflated and urges the workpiece against a contour surface corresponding to a desired configuration of the workpiece. Coolant fluid can also be circulated through the die cavity to cool the workpiece. Thus, the workpiece can be heated, formed, and cooled quickly and without substantial heating of other components, thereby reducing the time and energy relative to conventional forming methods.