Lanthanides have been investigated extensively for potential applications in quantum information processing and high-density data storage at the molecular and atomic scale. Experimental achievements include reading and manipulating single nuclear spins, exploiting atomic clock transitions for robust qubits and, most recently, magnetic data storage in single atoms. Single-molecule magnets exhibit magnetic hysteresis of molecular origin-a magnetic memory effect and a prerequisite of data storage-and so far lanthanide examples have exhibited this phenomenon at the highest temperatures. However, in the nearly 25 years since the discovery of single-molecule magnets, hysteresis temperatures have increased from 4 kelvin to only about 14 kelvin using a consistent magnetic field sweep rate of about 20 oersted per second, although higher temperatures have been achieved by using very fast sweep rates (for example, 30 kelvin with 200 oersted per second). Here we report a hexa-tert-butyldysprosocenium complex-[Dy(Cpttt)2][B(C6F5)4], with Cpttt = {C5H2tBu3-1,2,4} and tBu = C(CH3)3-which exhibits magnetic hysteresis at temperatures of up to 60 kelvin at a sweep rate of 22 oersted per second. We observe a clear change in the relaxation dynamics at this temperature, which persists in magnetically diluted samples, suggesting that the origin of the hysteresis is the localized metal-ligand vibrational modes that are unique to dysprosocenium. Ab initio calculations of spin dynamics demonstrate that magnetic relaxation at high temperatures is due to local molecular vibrations. These results indicate that, with judicious molecular design, magnetic data storage in single molecules at temperatures above liquid nitrogen should be possible.