We present near-infrared K-band (1.94--2.52 μm) spectroscopy of the deeply embedded protostellar source HOPS 370, obtained with the TIFR–ARIES Near Infrared Spectrometer (TANSPEC) on the 3.6-m Devasthal Optical Telescope (DOT). The spectrum is dominated by prominent molecular hydrogen (rm H₂) ro-vibrational emission, with multiple transitions detected from the 1--0 S, 2--1 S, and 1--0 Q branches. Using the intrinsically linked rm H₂ 1--0 Q(3) and 1--0 S(1) transitions, which arise from the same upper energy level, we derive a visual extinction of A_V = 23.24 ± 1.25 mag, corresponding to A_K = 2.50 ± 0.13 mag, consistent with the embedded Class 0/I nature of the source. The diagnostic line ratio F(2--1 rm S(1))/F(1--0 rm S(1)) = 0.12 ± 0.01 is consistent with thermal excitation and disfavors ultraviolet fluorescence as the dominant excitation mechanism. Assuming optically thin emission and local thermodynamic equilibrium, we derive an rm H₂ excitation diagram that yields an excitation temperature of 2078 ± 215 K and a molecular hydrogen column density of (1.93 ± 0.93)×10²⁰ cm⁻². We further derive an ortho-to-para ratio of 2.45 ± 0.21, indicating substantial shock-driven thermal processing while remaining below the high-temperature equilibrium value of 3. Taken together, these diagnostics indicate that the molecular hydrogen emission in HOPS 370 originates predominantly in warm, shock-heated gas most likely associated with its protostellar outflow. Our results demonstrate the diagnostic power of combined S- and Q-branch rm H₂ spectroscopy for constraining the physical conditions and excitation history of deeply embedded protostellar systems.