The electronic specific heat of ${\text{PrOs}}_{4}{\text{Sb}}_{12}$ was measured on different single crystals at temperatures down to 40 mK using a relaxation method. All investigated crystals exhibited a broad shoulder in specific heat near 0.4 K. This anomaly seems to be related to that found previously in Sb nuclear quadrupolar resonance study and possibly in lower critical-field and penetration-depth measurements. The onset of the specific-heat anomaly shows no response to magnetic fields as large as 0.2 T. These results imply a modification of superconducting properties (and normal-state properties) rather than appearance of a new superconducting phase at low temperatures. Our measurement detects low-temperature nuclear specific heat, which we suggest might be due to nuclear quadrupolar specific heat of Pr atoms, frozen in off-center positions.