Both amorphous and crystalline materials frequently exhibit low-temperature specific heats in excess of what is predicted using the Debye model. The signature of this excess specific heat is a peak observed in C/T3 versus T. To understand the curious absence of long-range ordering of local distortions in the crystal structure of pyrochlore Bi2Ti2O7, we have measured the specific heat of crystalline Bi2Ti2O7 and related compounds. We find that the peak in C/T3 versus T in Bi2Ti2O7 falls at a substantially lower temperature than other similar compounds consistent with the presence of disorder. This thermodynamic evidence for disorder in crystalline Bi2Ti2O7 is consistent with quenched configurational disorder among Bi lone pairs produced by the geometrical frustration, which could represent a possible realization of “charge ice.”