A method of and apparatus for reducing the rate at which the heat content of a cryogenic liquid such as liquefied oxygen or nitrogen increases as a consequence of its being necessarily shipped in a partially filled container. The method includes dividing a predetermined volume of the liquid which ordinarily would be loaded into a shipping container therefor into major and minor fractions, the first of which is significantly larger than the second. The major fraction is confined within a container compartment having substantially the same volume as that of the major fraction, and the minor fraction is confined within a container compartment having a substantially larger volume than that of the minor fraction so as to accommodate any enlargement in the volume of the major fraction as a consequence of increases in the heat content thereof. Any such increases in the volume of the major fraction are withdrawn from the container compartment confining the same and are delivered to the container compartment confining the minor fraction. The apparatus includes a tank car having a large container provided with inner and outer wall structures separated from each other to define a heat-insulated space therebetween. The container is subdivided by a bulkhead into major and minor compartments, and means are provided for filling the container with a cryogenic liquid and for withdrawing such liquid therefrom. The minor and major compartments are flow interconnected by valve-equipped conduits that enable any overflow of liquid from the major compartment resulting from temperature-induced volumetric increases in the liquid confined therein to pass into the minor compartment.