A method of and apparatus for continuously foaming a polyimide prepolymer powder which is not susceptible to heating by microwave energy utilize a preheated conveyor belt to heat the powder in contact with and adjacent the surface of the conveyor belt to commence the reaction and foaming of the powder as it enters an oven which further heats the powder by convection and infrared radiation to form a continuous foam bun. The conveyor belt is cooled as it exits the oven to cool a bottom surface of the foam product to enable the foam product to be removed from the conveyor before interior portions of the foam product have cooled. Foam adhering to the conveyor belt, after the product has been removed, is cleaned from the conveyor belt, collected and mixed with and used as a filler in the prepolymer powder used in the process. In addition the mass of the powder entering the oven and the density and degree of cure of the foam bun exiting the oven are monitored to continuously control the process.