Molecular interaction potentials are difficult to measure experimentally and hard to compute from first principles, especially for large systems such as proteins. It is therefore desirable to estimate the potential energy that underlies a thermodynamic ensemble from simulated or experimentally determined configurations. This inverse problem of statistical mechanics is challenging because the various potential energy terms can exhibit subtle indirect and correlated effects on the resulting ensemble. A direct approach would try to adapt the force field parameters such that the given configurations are highly probable in the resulting ensemble. But this would require a full simulation of the system whenever a parameter changes. We introduce an extension of the configurational temperature formalism that allows us to circumvent these difficulties and efficiently estimate interaction potentials from molecular configurations. We illustrate the approach for various systems including fluids and a coarse-grained protein model.