A broadband CARS system is constructed for shot by shot measurement of a full CARS spectrum, which consists of a frequency doubled Nd:Yag laser, broadband mode-less laser and optical multi-channel analyzer installed in a double grating monochromator. To increase the accuracy of CARS temperature measurement and get better the fitting goodness, we have measured the slit function of the detection system and determined the analytical functional form of the slit function. Accuracy of the CARS system for temperature measurement is evaluated from the difference between the best-fit temperature of CARS spectrum and temperature of thermocouple reading. The uncertainty of the temperature measurement is found to be less than 1.5% in temperature range from 300 K to 1300 K.