This paper investigates the possibility of a many-body localized phase in a one-dimensional lattice model of interacting spinless fermions in a random potential at high temperatures. The authors suggest that a localized phase at nonzero temperature T > 0 may exist even when both disorder and interactions are strong, and that this phase transition can be studied numerically through exact diagonalization of small systems. They analyze the spectral statistics of finite-size samples, finding that the statistics cross over from those of orthogonal random matrices in the diffusive regime to Poisson statistics in the localized regime. However, the data show deviations from simple one-parameter finite-size scaling, with the apparent mobility edge "drifting" as the system size increases. Based on spectral statistics alone, the authors are unable to make a strong numerical case for the presence of a many-body localized phase at nonzero T. The paper discusses the implications of this drift for the existence of a many-body localized phase at high temperatures. It suggests that the drift could indicate either a finite critical point or an infinite critical point, with the latter implying that the insulating phase does not exist at these high temperatures. The authors also note that the spectral statistics may not be a good tool for simple finite-size scaling analysis, and that other approaches to this problem may be needed in the future. The paper concludes that while some indications of the proposed many-body localization transition are clearly seen, there are strong deviations from and/or corrections to finite-size scaling, which may call into question the existence of the proposed many-body localized phase at the high temperatures studied.This paper investigates the possibility of a many-body localized phase in a one-dimensional lattice model of interacting spinless fermions in a random potential at high temperatures. The authors suggest that a localized phase at nonzero temperature T > 0 may exist even when both disorder and interactions are strong, and that this phase transition can be studied numerically through exact diagonalization of small systems. They analyze the spectral statistics of finite-size samples, finding that the statistics cross over from those of orthogonal random matrices in the diffusive regime to Poisson statistics in the localized regime. However, the data show deviations from simple one-parameter finite-size scaling, with the apparent mobility edge "drifting" as the system size increases. Based on spectral statistics alone, the authors are unable to make a strong numerical case for the presence of a many-body localized phase at nonzero T. The paper discusses the implications of this drift for the existence of a many-body localized phase at high temperatures. It suggests that the drift could indicate either a finite critical point or an infinite critical point, with the latter implying that the insulating phase does not exist at these high temperatures. The authors also note that the spectral statistics may not be a good tool for simple finite-size scaling analysis, and that other approaches to this problem may be needed in the future. The paper concludes that while some indications of the proposed many-body localization transition are clearly seen, there are strong deviations from and/or corrections to finite-size scaling, which may call into question the existence of the proposed many-body localized phase at the high temperatures studied.