We submit to consideration of the 7th framing EU program, Marie Curie Incoming Fellowshipprogram, a research project in the field of computational material science to explore material thermal properties of homogeneous systems. We propose this project with the idea of setting up long term collaborations between the groups in Mexico and Germany. The proposed research program is aimed to understand, to develop and to characterize systems with novel properties originating from electronic correlations and in particular of systems where the electron-phonon coupling plays an important role in its thermal response. In that respect, we expect to use and implement two different recent proposed methodologies, which allow us to explore the non adiabatic contribution and anharmonic effects to the phonon spectra. This physical phenomena has been reported to have relevance in layered materials, such as graphene, MgB2, CaC6 and in most superconductor systems. Basically we will be implementing, within the ELK code(elk.sourceforge.net), two different methodologies to characterize thermal behavior away from the adiabatic approximation (a) a self consistent phonon calculation, where the atoms within the unit cell are displaced by a Bose-Einstein factor, such that they are able to reach a new stable minima as function of temperature (b) a fist order perburbation on the changes on the stationary forces after a time dependent perburbationon the ionic displacements is imposed into the system.