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Only a handful of late-T brown dwarfs have been monitored for spectro-photometric variability, leaving incomplete the study of the atmospheric cloud structures of the coldest brown dwarfs, that share temperatures with some cold, directly-imaged exoplanets. 2MASSJ00501994-332240 is a T7.0 rapidly rotating, field brown dwarf that showed low-level photometric variability in data obtained with the Spitzer Space telescope. We monitored 2MASSJ00501994-332240 during ~2.6 hr with MOSFIRE, installed at the Keck I telescope, with the aim of constraining its near-infrared spectro-photometric variability. We measured fluctuations with a peak-to-peak amplitude of 1.48+\-0.75% in the J-band photometric light curve, an amplitude of 0.62+/-0.18% in the J-band spectro-photometric light curve, and an amplitude of 1.26+/-0.93% in the H-band light curve, and an amplitude of 5.33+/-2.02% in the CH_4-H_2O band light curve. Nevertheless, the Bayesian Information Criterion does not detect significant variability in any of the light curves. Thus, given the detection limitations due to the MOSFIRE sensitivity, we can only claim tentative low-level variability for 2M0050-3322 in the best-case scenario. The amplitudes of the peak-to-peak fluctuations measured for 2MASSJ00501994-332240 agree with the variability amplitude predictions of General Circulation Models for a T7.0 brown dwarf for an edge on object. Radiative-transfer models predict that the Na_2S and KCl clouds condense at pressures lower than that traced by the CH_4-H_2O band, which might explain the higher peak-to-peak fluctuations measured for this light curve. Finally, we provide a visual recreation of the map provided by General Circulation Models and the vertical structure of 2MASSJ00501994-332240 provided by radiative-transfer models.