Lineaments in the gravity field with wavelengths of 100–200 km affect the south-central Pacific. Because they align with absolute plate motion, it has been proposed that they reflect small-scale convection cells beneath the lithosphere that become elongated by basal shear. Alternatively, it was suggested that they reflect channelized flow of low viscosity material following the base of the lithosphere toward the East Pacific Rise, or that they result from lithospheric-scale thermal contraction cracks. Here, we report about previously undetected gravity lineaments across the Cocos Plate. Similarly to the south-central Pacific lineaments, the Cocos lineaments affect a plate that is anomalously shallow, with seamounts aligning mostly within their troughs. However, the Cocos lineaments strike markedly oblique to absolute plate motion and follow instead trajectories that are perpendicular to seafloor isochrons, a characteristic best explained by the thermal contraction crack model. The presence of steep scarps at the base of seamounts and the seismic imaging of faults striking perpendicular to isochrons further support this interpretation. Assuming that the slow subsidence rates of the south-central Pacific and Cocos plates reflect a warmer upper mantle, we propose that the associated thinner elastic plates favor the formation of thermal contraction cracks. A thinner elastic plate may also explain the pattern of ridge propagation in both areas. At large ridge offsets with a history of steady migration, the propagating segments have been those cutting into the shallower flanks, consistent with the concept that a warmer, thinner plate is more easily cracked.