Controlling thermoelastic anisotropy of liquid crystals (LCs) is important for achieving reliable structural stability and efficient heat dissipation, especially for high-performance LC devices. A solid understanding of the thermoelastic anisotropy and its relation with the LC molecular structure is, however, still missing. Here, we studied the direction-dependent mechanical and thermal properties of 5-n-octyl-2-(4-n-octyloxy-phenyl)-pyrimidine (PYP8O8) in a wide temperature range, covering five phases (i.e., crystalline, smectic C, smectic A, nematic, and liquid), by Brillouin light spectroscopy and temperature wave analysis, respectively. We found that the mechanical anisotropy is much smaller than the thermal anisotropy at LC phases; both anisotropies show strong phase dependence, with the biggest change occurring at the crystalline to LC phase transition; and the anisotropy of the phonon mean-free path correlates with the structural anisotropy of the rigid core of the LC molecule. The analysis of the temperature-dependent thermoelastic anisotropy of LCs yields insights into structure-based phonon engineering.