Laser-induced grating spectroscopy (LIGS) is applied, for the first time, to a swirling non-premixed hydrogen-air flame in a high-pressure combustion facility. A portable LIGS unit is used to probe 35 different axial and radial locations in the flame and a new conditioned processing approach based on laminar flame simulation is introduced to infer temperatures from instantaneous LIGS spectra. Thermal and electrostrictive frequencies are used to produce a spatial map of temperatures in the combustor. Temperatures up to $2,500$ K are measured in this work, which constitute the highest temperatures ever measured using LIGS. Challenges associated with the deployment of the technique in turbulent stratified hydrogen flames are discussed, as are potential measures to overcome them, including the use of data-driven clustering techniques.