I am not sure what do you expect from or how do you understand the temperature correction. The term N. Dragoe mentions is related to the model of thermal vibrations which smear the probability of atomic positions and reduce the intensity with 2theta. In fact, it corrects everything which has a similar effect on the XRD pattern. But as far as I know this term is OK and already considered in each serious software.

If you are looking for the impact of the temperature on the unit cell (anisotropic expansion coefficient), i.e. on the peak positions, I havn't heard that this is implemented in a software. However, this is actually not your question because you are looking for the integral intensity, or am I wrong?

Thank you Dr. Dragoe and Dr. Noize for the response. I found in many papers that people have used different softwares for obtaining this temperature correction . But I don't have any access of such kind of softwares for getting directly the correction, therefore, I wanted to calculate this manually.