The noise temperature and gain stability of the superconducting unbiased parametric amplifier (SUPARAMP) have been calculated. The results of the analysis suggest that extremely low-noise amplification of signals from cryogenic sources may be achieved. It seems possible to obtain an effective input noise temperature of 1 K for signal frequencies up to 10 GHz, having a stable power gain of 20–30 dB. This paper provides the fundamental design specifications necessary for the construction of a low-noise SUPARAMP.