From the first stages of star and galaxy formation , non-gravitational processes such as ram pressure stripping , SNs , galactic winds , AGNs , galaxy-galaxy mergers , etc… lead to the enrichment of the IGM in stars , metals as well as dust , via the ejection of galactic material into the IGM . We know now that these processes shape , side by side with gravitation , the formation and the evolution of structures . We present here hydrodynamic simulations of structure formation implementing the effect of the cooling by dust on large scale structure formation . We focus on the scale of galaxy clusters and study the statistical properties of clusters . Here we present our results on the T _ { X } - M and the L _ { X } - M scaling relations which exhibit changes on both the slope and normalization when adding cooling by dust to the standard radiative cooling model . For example , the normalization of the T _ { X } - M relation changes only by a maximum of 2 % at M = 10 ^ { 14 } Â M _ { \odot } whereas the normalization of the L _ { X } - T _ { X } changes by as much as 10 % at T _ { X } = 1 Â keV for models that including dust cooling . Our study shows that the dust is an added non-gravitational process that contributes shaping the thermodynamical state of the hot ICM gas .