Thermal contributions to the free energy have to be taken into account to rationalize the formation of Gd3N@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.