The purely electronic linewidth δ of terrylene impurity molecules in monocrystalline biphenyl is studied at temperatures T between 1.7 and 3.5 K using the technique of single-molecule spectroscopy (SMS). Based on the data obtained, individual molecules appear to have their own law of δ(T) dependence; further, hysteresis effects have been observed in thermocycling experiments. The single-molecule (SM) lines investigated quickly broaden and vanish at temperatures between 3 and 3.5 K and reappear after the sample is cooled down again. At T≈2 K, a slow process of spectral diffusion (SD) was observed on timescales longer than 10 s. To learn about the role of faster SD processes, the technique of intensity–time–frequency correlation (ITFC) SMS was applied to a stable SM line after it had been broadened by 75% as a result of a thermocycling experiment. At 2 and 2.3 K, no significant line broadening could be revealed on timescales between 0.16 ms and 10 s.