A new blood unit cooling system was designed to cool blood rapidly to about 22° C. and maintain it at about that temperature, even in ambient temperature extremes, for several hours. The system incorporating a preferred eutectic solution including 98% 1-dodecanol, 1.5% myristyl alcohol and 0.5% 1-decanol (having, a melting point of about 23° C.) contained in a sealed flexible polymer layer, was used to cool whole blood-filled bags. The preferred design uses inner and outer containers, each made of transparent polyethylene sheets, where the inner compartments are filled with the solution and sealed, and then placed into each compartment in an outer container, wherein two compartments in the outer container are separated by a flattened and sealed portion of the polyethylene.