Probing the rotational and translational diffusion and colloidal stability of nanorods is of significant fundamental interest with implications for many different applications. Recently R. Nixon-Luke and G. Bryant presented a method to analyze angle-dependent depolarized dynamic light scattering data allowing for the clear separation of the translational and rotational diffusion coefficients of gold nanorods in dilute suspension (R. Nixon-Luke and G. Bryant, Part. Part. Syst. Charact., 2018, 36, 1800388). In the present work we applied this analysis to gold nanorods decorated with high molecular weight, thermoresponsive poly-N-isopropylacrylamide ligands, which results in particles with lower effective aspect ratios. The temperature response of the ligand shell is studied. We precisely determine the translational and rotational diffusion coefficients over a broad range of temperatures and the results are compared to theoretical predictions. The results show that as temperature increases the ligands collapse, and the effective aspect ratio increases as the particle shape transitions from prolate spheroid at low temperatures to more cylindrical at high temperatures.