We have used quantum chemistry computations, in conjunction with isodesmic-type reactions, to obtain accurate heats of formation (HoFs) for the small fullerenes C-20 (2358.2 +/- 8.0 kJ mol(-1)), C-24 (2566.2 +/- 7.6), and the lowest-energy isomers of C-32 (2461.1 +/- 15.4), C-42 (2629.0 +/- 20.5), and C-54 (2686.2 +/- 25.3). As part of this endeavor, we have also obtained accurate HoFs for several mediumsized molecules, namely 216.6 +/- 1.4 for fulvene, 375.5 +/- 1.5 for pentalene, 670.8 +/- 2.9 for acepentalene, and 262.7 +/- 2.5 for acenaphthylene. We combine the energies of the small fullerenes and previously obtained energies for larger fullerenes (from C-60 to C-6000) into a full picture of fullerene thermochemical stability. In general, the per-carbon energies can be reasonably approximated by the "R+D" model that we have previously developed [Chan et al. J. Chem. Theory Comput. 2019, 15, 1255-1264], which takes into account Resonance and structural Deformation factors. In a case study on C-54, we find that most of the high-deformation-energy atoms correspond to the sites of the C-Cl bond in the experimentally captured C54Cl8. In another case study, we find that C-60 has the lowest value for the maximum local-deformation energy when compared with similar-sized fullerenes, which is consistent with its "special stability". These results are indicative of structural deformation playing an important role in the reactivity of fullerenes.