We have performed extensive transport experiments on a 4 nm thick aluminum (Al) superconducting film grown on a GaAs substrate by molecular beam epitaxy (MBE). Nonlinear current-voltage (I-V) measurements on such a MBE-grown superconducting nanofilm show that V ∼ I 3, which is evidence for the Berezinskii-Kosterlitz-Thouless (BKT) transition, both in the low-voltage (T BKT ≈ 1.97 K) and high-voltage regions (T BKT ≈ 2.17 K). In order to further study the two regions where the I-V curves are BKT-like, our experimental data are fitted to the temperature-induced vortices/antivortices unbinding model as well as the dynamical scaling theory. It is found that the transition temperature obtained in the high-voltage region is the correct T BKT as confirmed by fitting the data to the aforementioned models. Our experimental results unequivocally show that I-V measurements alone may not allow one to determine T BKT for superconducting transition. Therefore, one should try to fit one's results to the temperature-induced vortices/antivortices unbinding model and the dynamical scaling theory to accurately determine T BKT in a two-dimensional superconductor.