The present invention is directed to a medium for preserving cells at non-cryogenic freezing temperatures. The medium comprises a hydrophilic and nontoxic polymer or other macromolecule, an aqueous liquid, and a cryoprotectant. The molecules of the macromolecule form compact three-dimensional structures that are spherical in shape when dissolved in the aqueous liquid. The medium of the present invention can be used for long-term storage of cells at non-cryogenic temperatures with outcomes similar to those seen with storage at cryogenic temperatures.