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A comprehensive statistical analysis of the distributions of the adhesion strength (σ) developed during a long-term contact (up to 2 months) of two identical specimens of an amorphous entangled polymer at a very low temperature (T) of 24 °C with respect to the bulk glass transition temperature (Tg), below Tg by 80 °C, was carried out. For this purpose, two representative glassy polymers, polystyrene [PS; three PSs differing markedly in the number-average molecular weight (Mn) from 75 to 966 kg/mol] and poly(methyl methacrylate) (PMMA; Mn = 43.5 kg/mol), were selected. Keeping in contact the two specimens of PS or PMMA at T = 24 °C resulted in self-bonding at PS–PS and PMMA–PMMA interfaces. The as-self-bonded interfaces were shear fractured in tension to measure their σ values. The four σ distribution sets obtained for such a low T for the first time were examined using a number of common formal tests for normality and graphical statistical methods, including Weibull’s model. In general, the σ distributions for the PS with the highest Mn = 966 kg/mol were described more correctly than those for the other three polymers, regardless of the statistical methods applied. These results were compared with those obtained after self-bonding at a significantly higher T = Tg − 33 °C for the same polymers. The statistical parameters estimated at markedly different temperatures (T = Tg − 80 °C and Tg − 33 °C) were compared and discussed.