A method for preserving an extracorporeal organ during hypothermic transport of the organ. The method includes placing an organ in a self-purging preservation apparatus to suspend the sample in preservation fluid, and filling the apparatus with a cold preservation solution. The self-purging preservation apparatus is placed in an insulated transport container having a cooling medium. When assembled, the system allows for transport of biological samples for extended periods of time at a stable temperature, thereby increasing the distance that the organ can be transported without compromising organ function.