We demonstrate the feasibility of single laser shot CARS thermometry with simultaneous measurement of intensities of hydrogen Q-branch lines and their line widths in a pulsed CH4/O2 combustion chamber operating at 20 MPa pressure and 3000 K temperature – the parameters that are typical for full-scale rocket engines. The measurements were done by means of a spectrograph combined with an interferometer having orthogonal directions of dispersions. This approach allows correct temperature evaluation that takes into account directly measured line widths.