A cryostat for electron irradiations at liquid hydrogen or helium temperatures is described. The cryostat uses two concentric liquid coolant containers, of which the inner reservoir is sealed and acts as a heat exchanger through ebullition and recondensation of the coolant gas. This allows irradiations with a power input from the beam of up to a few watts, and when the sample is thermally isolated allows it to be annealed up to room temperature.