The viral capsid is a macromolecular complex formed by a defined number of self-assembled proteins, which, in many cases, are biopolymers with an identical amino acid sequence. Specific protein-protein interactions (PPI) drive the capsid self-assembly process, leading to several distinct protein interfaces. Following the PPI hot spot hypothesis, we present a conservation-based methodology to identify those interface residues hypothesized to be crucial elements on the self-assembly and thermodynamic stability of the capsid. We validate the predictions through a rigorous physical framework which integrates molecular dynamics simulations and free energy calculations by Umbrella sampling and the potential of mean force using an all-atom molecular representation of the capsid proteins of an icosahedral virus in an explicit solvent. Our results show that a single mutation in any of the structure-conserved hot spots significantly perturbs the quaternary protein-protein interaction, decreasing the absolute value of the binding free energy, without altering the protein's secondary nor tertiary structure. Our conservation-based hot spot prediction methodology can lead to strategies to rationally modulate the capsid's thermodynamic properties.