Thermal contributions to the free energy have to be taken into account to rationalize the formation of Gd(3)N@C(s)(39663)-C(82), a nitride endohedral metallofullerene that shows a carbon cage with two fused pentagons which is not predicted to have the lowest electronic energy among the isomers of C(82). The lower symmetry and the larger number of pyracylene units of C(s)(39663)-C(82) with respect to the cage in the lowest-energy metallofullerene, C(2v)(39705)-C(82), favor its formation at high temperatures, as seen for other similar cage isomers that encapsulate metal clusters within the C(80) and C(82) families. These cages, which share common motifs with the prototypical I(h)(7)-C(80), are all related by C(2) insertions/extrusions and Stone-Wales transformations.