The invention relates to a heat generator for well stimulation, comprising a tubular fuel vessel (22) with two or more mutually separated, closed segments (23) arranged in longitudinal succession and each at least partly filled with fuel (30), and at least one igniter (40) for ignition of the fuel in at least one of the segments (23), wherein the ends of the segments are connected such that the fuel in a subsequent segment is ignitable owing to the evolution of heat in the course of burnoff of the fuel in a preceding segment. The invention further relates to a process for well stimulation using an inventive heat generator.