Pump for conveying a cryogenic fluid

The pump has a cylinder (9) with a piston (11) arranged in the cylinder, where the piston carries out stroke movements running back and forth in the cylinder. A heating unit is provided for heating the fluid flowing from a low temperature chamber (13) into a high temperature chamber (15) through a fluid connection (25) during the former stroke movement, such that an isochoric pressure increasing with the temperature adjusts in the high temperature chamber and exceeds the container pressure.