Protein methyl groups can participate in multiple motional modes on different time scales. Sub-nanosecond to nano-second time scale motions of methyl axes are particularly challenging to detect for small proteins in solutions. In this work we employ NMR relaxation interference between the methyl H-H/H-C dipole-dipole interactions to characterize methyl axes motions as a function of temperature in a small model protein villin headpiece subdomain (HP36), in which all non-exchangeable protons are deuterated with the exception of methyl groups of leucine and valine residues. The data points to the existence of slow motional modes of methyl axes on sub-nanosecond to nanosecond time scales. Further, at high temperatures for which the overall tumbling of the protein is on the order of 2 ns, we observe a coupling between the slow internal motion and the overall molecular tumbling, based on the anomalous order parameters and their temperature-dependent trends. The addition of 28% (w/w) glycerol-d8 increases the viscosity of the solvent and separates the timescales of internal and overall tumbling, thus permitting for another view of the necessity of the coupling assumption for these sites at high temperatures.