Calculations of NMR shielding tensors and nuclear quadrupole coupling (NQC) tensors at the Kohn-Sham density functional level are used to simulate (27)Al magic-angle spinning (MAS) NMR spectra of the important olefin polymerization co-catalyst methylaluminoxane (MAO) at 77, 298, 398, and 498 K and spectrometer magnetic field inductions B ranging from 14.1 to 23.5 T. The calculations utilize the temperature (T) dependent distribution of species present in MAO determined recently by Zurek and coworkers from first-principles theory [Macromolecules, 2014, 47, 8556]. The NMR calculations suggest that variable-T and variable-B NMR measurements are able to quantify the ratio of free versus bound trimethyl-aluminum (TMA) in MAO via characteristic spectral features assigned to 3-coordinate and 4-coordinate Al sites in MAO as well as spectral features arising from free TMA or its dimer. The T-dependent distribution of species causes other characteristic features in the NMR spectra to appear/disappear that can be associated with different aluminum environments such as square vs. hexagonal faces in cage and tubular structures. The simulated spectra at 298 K and 19.6 T are in reasonably good agreement with the experimental solid-state NMR (SSNMR) spectra obtained previously for MAO gel. The promise and limitations of solid-state NMR to unravel the enigma surrounding the structure(s) of MAO are discussed.