Thermodynamic properties of matter e.g., melting point, are important for various applications. However, in some substances the primary observed effect upon heating is decomposition which in some cases is accompanied by fluidization. Thus, it would be very useful to be able to predict if a given substance will be able to melt or will exhibit melting inability upon heating. In this work, a thermodynamic explanation for the melting inability of molecular solids is provided and a corresponding criterion is proposed for the prediction of melting ability or inability of a given substance. One key concept is to study the strength of the weakest chemical bond rather than overall enthalpy of reaction. This arises from the fact that if decomposition occurs, then, regardless of the extent of decomposition, the transition cannot be considered to be melting. The criterion can be combined with sophisticated modeling in order to derive accurate values. Here, a simple method is proposed and an approximate index is developed which allows for a rapid and massive implementation of the criterion. The index is based on the concept of group contributions methods (estimation of the enthalpy of the maximum possible interactions, $\mathit{\Delta }{H}_{max}$) and on a distorted version of Trouton's rule (correlation of $\mathit{\Delta }{H}_{max}$ with the heat required for melting). The correlation factor ( $x_{melting}$) was found to be equal to 40.6%. The index is successfully applied in various organic substances, including (bio)molecules of pharmaceutical/nutraceutical interest. Index values between −30 and 0 correspond to marginal cases of rather high uncertainty. Positive index values clearly point out melting inability. The proposed index successfully predicts the melting ability/inability in more than 80% of the studied substances.