We present a calibration function in the general analytical form for the tropospheric temperature retrievals using pure rotational Raman (PRR) lidars. The function is derived within the framework of the semiclassical theory and takes into account the collisional broadening of all PRR lines. We analyze via simulation its four simplest nonlinear (three-coefficient) special cases to determine the function that yields the least error, and therefore, is the best-suited for the temperature retrievals. Two of them are proposed for the first time. The comparative analysis of temperature errors showed that all the special cases yield errors less than 0.1 K in modulus, and therefore, can be applied for the tropospheric temperature retrievals. The best function yields the maximum error less than 0.002 K in modulus and five times smaller compared to the commonly used nonlinear calibration function.