Thermal infrared (TIR) target tracking methods often adopt the correlation filter (CF) framework due to its computational efficiency. However, the low resolution of TIR images, along with tracking interference, significantly limits the performance of TIR trackers. To address these challenges, we introduce STARS, a novel sparse learning-based CF tracker that incorporates spatio-temporal regularization and super-resolution reconstruction. First, we apply adaptive sparse filtering and temporal regularization to extract key features of the target while reducing interference from background clutter and noise. Next, we introduce an edge-preserving sparse regularization method to stabilize target features and prevent excessive blurring. This regularization integrates multiple terms and employs the alternating direction method of multipliers to optimize the solution. Finally, we propose a gradient-enhanced super-resolution method to extract fine-grained TIR target features and improve the resolution of TIR images, addressing performance degradation in tracking caused by low-resolution sequences. To the best of our knowledge, STARS is the first to integrate super-resolution method within a sparse learning-based CF framework. Extensive experiments on the LSOTB-TIR, PTB-TIR, VOT-TIR2015, and VOT-TIR2017 benchmarks demonstrate that STARS outperforms state-of-the-art trackers in terms of robustness.