Accurate measurement of atomic temperature is fundamental for a wide range of applications, from quantum sensing to precision metrology. In optical lattice clocks, precise characterization of atomic temperature is required to minimize systematic uncertainties at the 10⁻¹⁸ level. In this work, we investigate atomic temperature measurements in the ytterbium optical clock developed at INRIM, IT-Yb1, employing sideband and transverse Doppler spectroscopy across a wide range of trapping conditions in a one-dimensional optical lattice. By implementing clock-line-mediated Sisyphus cooling [Phys. Rev. Lett. 133, 053401 (2024)], we reduce the atomic temperature and enable operation at shallower lattice depths down to D = 50 ER, where ER is the photon recoil energy. We compare temperature estimates obtained from the perturbed harmonic oscillator model with those derived using a Born-Oppenheimer model [Phys. Rev. A 101, 053416 (2020)]. Discrepancies of up to a factor of four are observed between the temperature estimates obtained with the two approximations. We assess the impact of these modeling differences on the evaluation of lattice light shifts and find relative frequency deviations of up to 8×10⁻¹⁷. Although sufficiently low atomic temperatures and the consistent use of theoretical models reduce these discrepancies to the low 10⁻¹⁸ level, these results motivate further investigations that will be relevant to state-of-the-art optical lattice clocks.