This data release provides a recursive-estimation framework to infer groundwater/surface-water exchange based on temperature time series collected at different vertical depths below the sediment/water interface. A heat-transport problem was formulated as a state-space model (SSM), in which the spatial derivatives in the convection/conduction equation are approximated using finite differences. The SSM is calibrated to estimate time-varying specific discharge using the Extended Kalman Filter (EKF) and Extended Rauch-Tung-Striebel Smoother (ERTSS) algorithms. This data release contains both algorithms, synthetic and field-experimental data, as well as VFLUX model results (Neversink_obs.csv, VFLUX_results.csv) used for validation and comparison. The tempest1d.py file contains the code to run the algorithm, while the compressed notebooks folder contains both ipython notebooks (.ipynb) and html versions of worksflows for algorithm application to provided data. More detailed instructions can be found in the readme.txt file attached.