We report on the application of coherent Rayleigh scattering (CRS) to the measurement of temperature in a flame using narrow bandwidth pump and probe fields. High resolution measurements of the line shape were used to derive flame temperature based on fits to the line shape. An uncertainty in the temperature of 3% was determined utilizing a CRS model that includes scattering from a multicomponent gas for the first time. This model was validated at room temperature for a mixture of atomic and molecular species.