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Infrared video has been of great interest in visual tasks under challenging environments, but often suffers from severe atmospheric turbulence and compression degradation. Existing video super-resolution (VSR) methods either neglect the inherent modality gap between infrared and visible images or fail to restore turbulence-induced distortions. Directly cascading turbulence mitigation (TM) algorithms with VSR methods leads to error propagation and accumulation due to the decoupled modeling of degradation between turbulence and resolution. We introduce \textbf{HATIR}, a \textbf{H}eat-\textbf{A}ware Diffusion for \textbf{T}urbulent \textbf{I}nfra\textbf{R}ed Video Super-Resolution, which injects heat-aware deformation priors into the diffusion sampling path to jointly model the inverse process of turbulent degradation and structural detail loss. Specifically, HATIR constructs a Phasor-Guided Flow Estimator, rooted in the physical principle that thermally active regions exhibit consistent phasor responses over time, enabling reliable turbulence-aware flow to guide the reverse diffusion process. To ensure the fidelity of structural recovery under nonuniform distortions, a Turbulence-Aware Decoder is proposed to selectively suppress unstable temporal cues and enhance edge-aware feature aggregation via turbulence gating and structure-aware attention. We built FILR-IVSR, the first dataset for turbulent infrared VSR, comprising paired LR-HR sequences from a FILR T1050sc camera ((1024 \times 768)) spanning 645 diverse scenes with varying camera and object motion conditions. This encourages future research in infrared VSR.
