The double-differential scattering cross section for a nucleus with pronounced resonances can be calculated using the stochastic method called Doppler Broadening Rejection Correction (DBRC). Its analytical formulation was developed by Rothenstein and Dagan. Both methodologies are based on the Free Gas Model (FGM), so they exclude chemical binding effects. The numerical instability of including chemical bounds can be balanced by the uncoupled phonon approximation (UPA). However, Courcelle showed that the UPA does not asymptotically resume the FGM and proposed an alternative model for correcting the asymptotic form. Preliminary tests on the Courcelle model showed inconsistent results in differential cross sections compared with the DBRC option of Monte Carlo codes in the framework of the FGM. In this work, a corrected version of Courcelle’s model is presented and applied in the FGM to 238U cross sections. The double-differential scattering cross sections calculated at 300 and 1474 K are in good agreement with those provided by the DBRC. The corrected model is consistent with angle-integrated scattering cross sections calculated with NJOY. The introduction of the effective temperature via the Short Collision Time approximation demonstrates the need to use a more complex model to account for crystalline effects.