Neutron-diffraction data presented in this paper demonstrate the relevance of lattice displacement above T_C, in our understanding of the evolution of the crystal structure with temperature in the layered colossal magnetoresistance manganite La_1.2Sr_1.8Mn₂O₇. The anomalous temperature behavior of thermal diffuse scattering in La_1.2Sr_1.8Mn₂O₇ strongly suggests that it arises from lattice displacements and correlates directly with anomalies in the displacement parameters of the O and Mn atoms and the Mn-O bond lengths. From our measurements, the insulator-metal transition can be described as a transition from a high-temperature state with disordered Mn-O bond lengths to a low-temperature state with a more uniform distribution on Mn-O bonds. These observations are in agreement with polaronic charge transport above T_C in the perovskite manganites; as electron hopping is responsible for bond disorder above T_C, below the transition where e_g carriers are delocalized, any lattice displacements are uniformly averaged.