Light-induced radical pairs in cryptochrome proteins located in the retina are thought to be thereceptors at the heart of the magnetic compass sense of migratory songbirds. Reliable simulations of the performance of such sensors face several fundamental challenges. The quantum spin dynamics of large spin systems must be modeled for periods in excess of a microsecond including realistic local magnetic interactions that fluctuate on a picosecond to microsecond time scale as a result of thermal motion. Here we employ newly developed computational methods that combine explicitly time-dependent internal magnetic interactions, obtained from molecular dynamics simulations and electronic structure calculations, with efficiently and accurately modeled spin dynamics of multinuclear electron-nuclear spin systems. We identify the range of frequencies of molecular motions that are expected to have the greatest effects on the sensitivity of the proposed compass to the direction of an Earth-strength magnetic field and obtain new insights into the potential enhancements in detection sensitivity afforded by thermal modulations of electron-nuclear hyperfine interactions.