We discuss a paradox from the field of relativistic thermodynamics: Two heat reservoirs of the same proper temperature move against each other. One is at rest in reference frame SA, the other in reference frame SB. For an observer, no matter in which of the two reference frames he is at rest, the temperatures of the two reservoirs are different. One might therefore conclude that a thermal engine can be operated between the reservoirs. However, the observers in SA and SB do not agree upon the direction of the entropy flow: from SA to SB, or from SB to SA. The resolution of the paradox is obtained by taking into account that the drive of an entropy current is not simply a temperature difference, but the difference of a quantity that depends on temperature and on velocity.