Temperature represents the atmospheric thermodynamic state. Measure the atmospheric temperature accurately and precisely is very important to understand the physics of the atmospheric process. Lidar has some advantages in the atmospheric temperature measurement. Based on the lidar equation and the theory of pure rotational Raman (PRR), we’ve simulated the temperature measurement errors of the double-grating-polychromator (DGP) based PRR lidar. First of all, without considering the attenuation terms of the atmospheric transmittance and the range in the lidar equation, we’ve simulated the temperature measurement errors which are influenced by the beam splitting system parameters, such as the center wavelength, the receiving bandwidth and the atmospheric temperature. We analyzed three types of the temperature measurement errors in theory. We’ve proposed several design methods for the beam splitting system to reduce the temperature measurement errors. Secondly, we simulated the temperature measurement error profiles by the lidar equation. As the lidar power-aperture product is determined, the main target of our lidar system is to reduce the statistical and the leakage errors.