In order to simply and safely transport a sample of semen, the semen is mixed and diluted with a dual sugar (sucrose and glucose) extender in a ratio of up to 10:1 (v/v) by inducting the semen into a semen storage device, e.g., a large volume syringe, having extender therein and optionally disposed within a form-fitting, radiation blocking, sleeve. The semen storage device is placed on a support member located on the floor of a rigid foamed plastic container. A refrigerant containing a solid foam coolant is placed in the container at a level that is higher than the semen sample, and the container is closed using a lid having a central boss that fits snugly into the mouth of the container. The lid has a continuous ridge that fits into a recess formed in the upper edge of the container. The closed container is then placed in a light weight double-walled cardboard box that exhibits considerable structural strength, increases the insulation, absorbs ambient moisture and protects the rigid foamed plastic container during transit. In the case a thermoregulating plate is disposed between the refrigerant and the semen sample, a cooling rate achieved by the present invention is no more than about 0.20.degree. C./min, preferably about 0.10.degree. C./min, and most preferably about 0.01.degree. C./min, over a temperature range of about 38.degree. C. to about 5.degree. C., preferably from about 15.degree. C. to about 5.degree. C. The optimum transport temperature of the semen sample during transport is preferably about 5.degree. C. to about 10.degree. C., most preferably about 7.5.degree. C. to about 8.5.degree. C. As an alternative to the thermoregulating plate, it is possible to interpose a bag or container of thermal ballast, e.g., water or a gel-like fluid, between the semen sample and the refrigerant or dilute the sample with sufficient extender that the spermatozoa are covered with a layer of liquid that is sufficiently thick as to protect them from thermal shock.