A thermodynamic assessment of the KF-ThF₄ binary system using the CALPHAD method is presented, where the liquid solution is described by the modified quasichemical formalism in the quadruplet approximation. The optimization of the phase diagram is based on experimental data reported in the literature and newly measured X-ray diffraction and differential scanning calorimetry data, which have allowed to solve discrepancies between past assessments. The low temperature heat capacity of α-K₂ThF₆ has also been measured using thermal relaxation calorimetry; from these data the heat capacity and standard entropy values have been derived at 298.15 K: C_p,m^o(K₂ThF₆,cr,298.15K)=(193.2±3.9) J·K^-1·mol^-1 and S_m^o(K₂ThF₆,cr,298.15K)=(256.9±4.8) J·K^-1·mol^-1. Taking existing assessments of the relevant binaries, the new optimization is extrapolated to the ternary systems LiF-KF-ThF₄ and NaF-KF-ThF₄ using an asymmetric Kohler/Toop formalism. The standard enthalpy of formation and standard entropy of KNaThF₆ are re-calculated from published e.m.f data, and included in the assessment of the ternary system. A calculated projection of the NaF-KF-ThF₄ system at 300 K and the optimized liquidus projections of both systems are compared to published phase equilibrium data at room temperature and along the LiF-LiThF₅ and NaF-KThF₅ pseudobinaries, with good agreement.