DFT calculations are utilized to compare and contrast the substituted aluminum-heterofullerenes, C20-nAln (with n=1-5) from thermodynamically view point, at density functional theory (DFT). Vibrational frequency analysis confirms that apart from C15Al5, all studied species are true minima. Considering the optimized geometries shows that all heterofullerenes are isolated-pentagon cage and none collapse to open deformed as segregated structure. The highest binding energy (5.56 eV/atom) and absolute heat of atomization (3323.68 kcal mol(-1)) reveals open-shell C19Al1 as the most stable thermodynamic heterofullerene. The most NICS (0) (isotropic and anisotropic parameters, -49.58 and -46.47 ppm, respectively) introduces closed-shell C18Al2-2 as the most aromatic structure. Also, closed-shell C16Al4-1 heterofullerene emerges with the most polarizability (307.71 a.u.) and hence activity to interact with the surrounding polar species. The lowest and the highest charge transfer on the surfaces of C-20 and C16Al4-2 without weak Al-Al bond, as the worst and the best candidate, respectively, provokes further investigation on impossible and possible application for hydrogen storage, respectively. We wish that the present survey will stimulate new experiments.