Various embodiments of the present invention disclose processes and systems for the off-line in-vitro purification of plasma harvested from a patient. In an embodiment of a process, in a first step cellular components are capable of being eliminated by membrane plasma separation at temperatures sufficiently high to avoid formation of a cryoaggregates, and in a second step the resulting plasma solution is cooled to a temperature that allows the formation of cryoaggragated molecules, but no formation of a cryogel.