Smart buildings use occupancy sensing for various tasks ranging from energy-efficient HVAC and lighting to space-utilization analysis and emergency response. We propose a people counting system which uses a low-resolution thermal sensor. Unlike previous people-counting systems based on thermal sensors, we use an overhead tripwire configuration at entryways to detect and track transient entries or exits. We develop two distinct people counting algorithms for this configuration. To evaluate our algorithms, we have collected and labeled a low-resolution thermal video dataset using the proposed system. The dataset, the first of its kind, is public and available for download. We also propose new evaluation metrics that are more suitable for systems that are subject to drift and jitter.