We construct a mobile broadband coherent anti-Stokes Raman spectroscopy system to measure the temperature of combustion gases. To improve the accuracy of CARS temperatures due to Stokes lasers, a modeless dye laser is constructed. A monochromator to disperse CARS spectra is also constructed in the spectrometer for easy portability. The accuracy of CARS temperature, measured in graphite tube furnace in reference to a radiation pyrometer, is better than 2 % from 1000 K to 2400 K. The CARS temperature error due to the variation of the spectral distribution of the modeless laser is measured to be less than 1.5 % during five hours operation. As a demonstration of combustion diagnosis, we applied the spectrometer to measure the temperature distribution of the propane air premixed flame.