The development of new thin-film photovoltaic (PV) absorbers is often hindered by the search for an optimal heterojunction contact; an unoptimized contact may be mistaken for poor quality of the underlying absorber, making it difficult to assess the reasons for poor performance. Therefore, quantifying the loss in device efficiency and open-circuit voltage (VOC) as a result of the interface is a critical step in evaluating a new material. In the present work, we fabricate thin-film PV devices using cuprous oxide (Cu2O), with several different n-type heterojunction contacts. Their current-voltage characteristics are measured over a range of temperatures and illumination intensities (JVTi). We quantify the loss in VOC due to the interface and determine the effective energy gap at the interface. The effective interface gap measured by JVTi matches the gap measured by X-ray photoelectron spectroscopy, albeit with higher energy resolution and an order of magnitude faster. We discuss potential artifacts in JVTi measurements and areas where analytical models are insufficient. Applying JVTi to complete devices, rather than incomplete material stacks, suggests that it can be a quick, accurate method to assess the loss due to unoptimized interface band offsets in thin-film PV devices.