Previously we investigated the kinetics of transient logarithmic creep of β–tin single crystals at very low temperatures 0.5K<T<4.2K with the sample under deformation in the normal (N) electronic state. In a continuation of that research, here we determine the boundary temperature Tg≈1.3K separating the regions of thermally activated (T>Tg) and quantum (T<Tg) plasticity governed by the motion of dislocations through Peierls barriers. Experiments are done on samples in the superconducting (S) state (0.5K<T<Tc=3.7K). It is shown that the NS transition preserves the logarithmic type of creep, its quantum character in the region T<Tg, and the value of the boundary temperature (TgS≈TgN≈1.3K). Analysis of the curves of the logarithmic creep in the quantum region can yield empirical estimates for the work hardening coefficient κ of the samples. It is found to increase significantly at the NS transition: along the whole deformation curve the work hardening in the S state occurs more intensely, and, on the average, κS≈1.5κN. Such an effect has been observed previously in a study of the plasticity of a series of fcc metals by the method of active deformation at a constant rate (V. V. Pustovalov, I. N. Kuz’menko, N. V. Isaev, V. S. Fomenko, S. É. Shumlin, Fiz. Nizk. Temp. 30, 109 (2004) [Low Temp. Phys. 30, 82 (2004)]). A comparison of the results of this study with previous results suggests that the increase in intensity of the work hardening at the superconducting transition is of a general nature for metallic superconductors and is manifested for other deformation regimes as well. The possible causes of the effect are discussed in the general conceptual framework of dislocation physics.