An anomaly of heat capacity near 70 K was registered in the crystalline L-cysteine (orthorhombic polymorph) by adiabatic calorimetry as a small, 3-5% height, diffuse "jump", or a wide "hump" accompanied by the substantial increase in the thermal relaxation time. The C-p(T) dependence is characteristic for a transformation extended over a wide temperature range and sensitive to the thermal prehistory of the sample, that can be interpreted as nonsimultaneous changes in the dynamics and the orientation of the numerous thiol groups in the structure. The measurements of the cell parameters and cell volume on cooling suggest that a discontinuity in their values over the transition point exists.