The heat capacity of the fast ion conductor BaSnF 4 was measured over the temperature range 7 < T< 345 K using adiabatic calorimetry. Our results show that a phase transition is not present. However, an anomalous rise in the molar heat capacity, Cp,m, occurs in the region 210 < T< 310 K; the entropy change of this rise amounts to AS/R=O.112. This anomaly coincides with the temperature range where a break in the slope of the electrical conductivity has been observed, which results in a threefold decrease in the activation energy required in the temperature region above the break at 272 K. Standard molar thermodynamic functions are presented at selected temperatures from 5 to 345 K.