Our micromechanical experiments show that viscoelastic features of type-I collagen fibril at physiological temperatures display essential dependence on the frequency and speed of heating. For temperatures of 20–30 ^°C the internal friction has a sharp maximum for a frequency less than 2 kHz. Upon heating the internal friction displays a peak at a temperature T_soft(v) that essentially depends on the speed of heating v: T_soft≈70^°C for v=1^°C/min, and T_soft≈25^°C for v=0.1^°C/min. At the same temperature T_soft(v) Young's modulus passes through a minimum. All these effects are specific for the native state of the fibril and disappear after heat-denaturation. Taken together with the known facts that the fibril is axially ordered as quasicrystal, but disordered laterally, we interpret our findings as indications of a glassy state, where T_soft is the softening transition.