Most molecules access a broad range of conformations at room temperature. Since electron-tunneling interactions are exponentially sensitive to geometry changes, thermal fluctuations are expected to have a large influence on room-temperature tunneling currents and scanning tunneling microscope images. We explore the influence of conformational freedom on tunneling currents in a simple model for tunneling mediated by a single small molecule that bridges between a model tip and substrate. The tip and substrate are described as semi-infinite structures. The bridging molecule and the metals are all described with tight-binding Hamiltonians. The conformationally averaged tunneling matrix element, proportional to the tunneling currents, is computed from thermally accessible molecular conformations. We vary the sulfur-to-sulfur separation distance in -S-(CH2)(8)-S- (n-octanedithiol) and, at each of these separations, compute the family of thermally accessible conformers. The two sulfur atoms are constrained to positions along a line perpendicular to the substrate surface. The conformationally averaged tunneling current computed for each fixed sulfur-to-sulfur distance is predicted to display an average distance dependence that is strikingly similar to the decay found in experiments performed on families of extended ("all trans") n-alkanes. That is, the tunneling current is predicted to decay exponentially with a decay parameter of similar to1.0 Angstrom(-1) based on the tip to substrate distance. This observation supports the notion that the most strongly coupled conformers in the ensemble dominate the STM tunneling current. This conclusion is also consistent with the analysis of protein electron-transfer systems, where thermal fluctuations are predicted to shorten coupling pathways and to minimize the influence on the rate of destructive interferences among multiple coupling pathways.