Hot cracking is a serious defect that may appear in steels during solidification due to thermal and mechanical stresses which break the thin liquid films between the dendrites. This contribution proposes a new, purely thermodynamics-based computational approach to assess the hot cracking susceptibility of Fe-C-Mn alloys using MatCalc, a CALPHAD-driven software. The ME-Fe database was used to simulate non-equilibrium solidification under Scheil-Gulliver conditions for nine alloy compositions ranging in 0.10-0.80 wt.% C and 0.50-1.50 wt.% Mn. Key parameters comprising the thermodynamic output are freezing range, final liquid fraction, solidification path angle, and final liquid composition. From these parameters, a composite Hot-Cracking Index (HCI) was formulated which may be applied to classify these alloys into susceptibility categories. Carbon was found to be the most prevailing factor; increasing C widens the solidification range and strengthens solute segregation. Manganese had a weaker but still noticeable effect, mainly due to its strong control of the persistence of the final liquid film. A high-risk composition was identified close to 0.80C-1.5Mn, while a safer region was found around 0.10C-1.0Mn. The approach is simple, reproducible, and provides an opportunity for material selection based on thermodynamic behavior; it therefore contributes significantly to alloy design and gives useful guidance for future experimental investigations.