The high-speed electron beam heating and the subsequent cooling processes in an amorphous semiconductor target of a beam memory have been studied by computer simulation. Such a memory would utilize the amorphous and the crystalline phases of chalcogenide thin films as the binary states of the memory. For an electron source of 1-µ radius, the results suggest that a storage target, consisting of a chalcogenide thin film whose thickness is twice the electron penetration range on a good heat sinking substrate, is the optimum target configuration. Possible high-speed memory operating characteristics with present long-life high-brightness electron guns are described.