•DSC measurements of the LiCl-UCl3, NaCl-UCl3, KCl-UCl3, LiCl-NaCl-UCl3, and NaCl-KCl-UCl3 salts.•Thermodynamic assessment of the LiCl-NaCl-KCl-UCl3 salt.•Heat capacity predictions of alkali uranium chloride molten salts.•Uncertainty assessment of DSC measurements.•High temperature XRD to suggest intermediate compound in NaCl-UCl3 system. Thermodynamic descriptions of higher-order molten salt systems are essential for the effective application of molten salt technologies. However, for pyroprocessing and molten salt reactor development, a complete description of the key Li-Na-K-U(III) chloride system has yet to be provided. To remedy this, we applied the CALculation of PHAse Diagrams (CALPHAD) approach to all available phase equilibria and related thermodynamic measurements that include new differential scanning calorimetry (DSC) observations for pseudo-binary and pseudo-ternary systems to obtain consistent and accurate sets of thermodynamic properties. An outcome of that effort was the apparent discovery of a previously unreported intermediate compound in the NaCl-UCl3 system. In this effort, we adopted a unique approach to the quantification of uncertainty in phase equilibria obtained from DSC measurements, which can provide distinct advantages in phase diagram analysis. The methodology indicates that reported values of uncertainty are often underestimated. The assessed systems of the current effort were incorporated in the publicly available Molten Salt Thermal Properties Database - Thermochemical.