Simone, I think GCM at the moment do are not able to take into account small effects as the aerosol heating rate. This is related to the indirect and semi-direct aerosol effects, and to my knowledge this is still matter of study for microphysical models, not GCM... Anyway I am not a modelist, and maybe some parameterizations have been developed. So, if anyone has a more precise answer, I am curious too!