Fullerene-based materials are widely used as acceptor and electron transport layer materials in organic and planar perovskite solar cells. Modeling of electronic properties such as band alignment and charge transport for these applications is typically done using optimized geometries. Here, we estimate the effects of nuclear motions on band structure, and electron and hole transport in two prototypical fullerenes, C60 and C70. We model the dynamics in solid fullerenes using Density Functional Tight Binding and we use the Density Functional Theory based Projection of Monomer Orbitals on Dimer Orbitals (DIPRO) approach to estimate the effects on the charge transfer integral in the Marcus approximation. We show that room-temperature molecular dynamics cause a shift and spread of frontier orbital energies on the order of 0.1 eV, which leads to an increase by more than a factor of two in the Marcus exponent, and can cause a decrease by up to orders of magnitude in the overlap integral, leading, in most cases, to an overall decrease in the charge transport rate.