A combined X-ray powder diffraction (XPD) and high-resolution extended X-ray absorption fine structure (EXAFS) at the Co and Ga K-edges study has been performed for LaCoO₃ and LaGaO₃ ceramics, the latter sample was used as a reference without spin transitions. Based on the X-ray diffraction data, we have found that isotropic atomic displacement parameters (ADP) or mean-squared displacement of the Co–O bond exhibit gradual growth below ~50 K, wherein the strain dependencies testify rapid increase below 150 K for the LaCoO₃ having rhombohedral structure. No similar features could be observed for LaGaO₃ sample. Above ~100 K the isotropic ADP of the Co–O bond indicate a gradual growth, whereas strain curves show distinct bend near the spin-state transition temperature at about 150 K. According to the EXAFS data, the correlated parallel mean squared relative displacement (MSRD_||) of Co–O and Ga–O bonds exhibit a gradual growth above 150 K; however, in the LaCoO₃ this parameter is notably bigger. It is supposed that at low temperature the cobalt ions are dominantly in low-spin (LS) state, while certain amount of Co³⁺ ions located within the surface layer of the crystallines have high-spin state (HS). Temperature growth leads to a gradual transformation of the HS state of the cobalt ions into the highly-hybridized intermediate-spin (IS) state, while the cobalt ions located in the inner part of the crystallines remain LS configuration up to 150 K. Further temperature increase leads to a spin transition of the Co³⁺ ions located within the crystallines from the LS state into the IS one.