Atmospheric turbulence severely degrades video quality by introducing distortions such as geometric warping, blur, and temporal flickering, posing significant challenges to both visual clarity and temporal consistency. Current state-of-the-art methods are based on transformer, 3D architectures and require multi-frame input, but their large computational cost and memory usage limit real-time deployment, especially in resource-constrained scenarios. In this work, we propose ReMATF, a lightweight recurrent framework that restores videos using only two frames at a time while preserving spatial detail and temporal stability. ReMATF combines a multi-scale encoder-decoder with temporal warping and a motion-adaptive temporal fusion module that performs per-pixel fusion between the warped previous output and the current prediction to enhance coherence without enlarging the temporal window. This design reduces flicker, sharpens details, and remains efficient. Experiments on synthetic and real turbulence datasets show consistent improvements in PSNR/SSIM and perceptual quality (LPIPS), along with substantially faster inference than multi-frame transformer baselines, making ReMATF suitable turbulence mitigation in resource-constrained scenarios.