The anisotropy of thermal diffusivity in four homologues of (p-alkoxybenzylidene)-p'-octylaniline (nO.8, n = 4 - 7) was measured using a temperature wave method. The results show that the thermal diffusivity component along the director (α(∥)) is considerably larger than that perpendicular to the director (α(⊥)) in all mesophases, i.e., nematic (N), smectic A (SmA), smectic B (SmB), and smectic G (SmG) phases. Both components of the thermal diffusivity show a dip at the second- or weakly first-order N-SmA phase transition due to the heat capacity anomaly. In contrast, at the first-order SmA-SmB phase transition, thermal diffusivity exhibits a stepwise increase. The x-ray and calorimetric measurements enable a calculation of the thermal conductivity and the study of the effect of the molecular length on the thermal conductivity and diffusivity in the SmA and SmB phases. For the homologues n = 4, 5, and 6, which exhibit the same phase sequence upon cooling, the parallel component of the thermal conductivity k(∥) in the SmA and SmB phases systematically increases with increasing length of the molecular tails, while no such increase is observed in the thermal diffusivity α(∥). We thus conclude that the molecular model [Urbach et al., J. Chem. Phys. 78, 5113 (1983)] is valid for the qualitative prediction of the effect of the molecular length on the magnitude of the thermal conductivity.