Förster Resonance Energy Transfer (FRET) is the incoherent transfer of an electronic excitation from a donor fluorophore to a nearby acceptor. FRET has been applied as a probe of local chromophore environments and distances on the nanoscale by extrapolating transfer efficiencies from standard experimental parameters, such as fluorescence intensities or lifetimes. Competition from nonradiative relaxation processes is often assumed to be constant in these extrapolations, but in actuality, this competition depends on the donor and acceptor environments and can, therefore, be affected by conformational changes. To study the effects of nonradiative relaxation on FRET dynamics, we perform two-dimensional electronic spectroscopy (2DES) on a pair of azaboraindacene (BODIPY) dyes, attached to opposite arms of a resorcin[4]arene cavitand. Temperature-induced switching between two equilibrium conformations, vase at 294 K to kite at 193 K, increases the donor-acceptor distance from 0.5 nm to 3 nm, affecting both FRET efficiency and nonradiative relaxation. By disentangling different dynamics based on lifetimes extracted from a series of 2D spectra, we independently observe nonradiative relaxation, FRET, and residual fluorescence from the donor in both vase to kite conformations. We observe changes in both FRET rate and nonradiative relaxation when the molecule switches from vase to kite, and measure a significantly greater difference in transfer efficiency between conformations than would be determined by standard lifetime-based measurements. These observations show that changes in competing nonradiative processes must be taken into account when highly accurate measurements of FRET efficiency are desired.