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.