The method for determining gas distribution function is reconstructed. In this study, theBoltzmann equation is bypassed by converse method. The temperature change is specified first inorder to determine the distribution function. The argument of this method is explained both byanalytically solving Bolztmann equation and pure probabilistic consideration in statisticalthermodynamics. Boltzmann equation is solved by modeling collision terms with severalassumptions and It is found that the results are similar. On the other hand, probabilistic methodgives no rigorous physical understanding so it offer several justifications about the resultingdistribution function. The calculation shows that the distribution function is totally Maxwellian inall cases. The temperature dependency only affects the peak value and the shape curve. It is foundthat more slender curve is resulted in higher temperature and quick sampling data is required toprobe the rapidly change temperature processes.