Concrete asphalt is a hydrocarbon material that includes a mix of mineral components along with a bituminous binder. Prior to mixing, its production protocol requires drying and heating the aggregates. Generally performed in a rotary drum, these drying and heating steps within mix asphalt processes have never been studied from a physical perspective. We are thus proposing in the present paper to analyze the drying and heating mechanisms when granular materials and hot gases are involved in a co-current flow. This process step accounts for a large proportion of the overall energy consumed during hot-mix asphalt manufacturing. In the present context, the high energy cost associated with this step has encouraged developing new strategies specifically for the drying process. Applying new asphalt techniques so that an amount of moisture can be preserved in the asphalt concrete appears fundamental to such new strategies. This low-energy asphalt, also referred to as the "warm technique", depends heavily on a relevant prediction of the actual moisture content inside asphalt concrete during the mixing step. The purpose of this paper is to present a physical model dedicated to the evolution in temperature and moisture of granular solids throughout the drying and heating steps carried out inside a rotary drum. An initial experimental campaign to visualize inside a drum at the pilot scale (i.e. 1/3 scale) has been carried out in order to describe the granular flow and establish the necessary physical assumptions for the drying and heating model. Energy and mass balance equations are solved by implementing an adequate heat and mass transfer coupling, yielding a 1D model from several parameters that in turn drives the physical modeling steps. Moreover, model results will be analyzed and compared to several measurements performed in an actual asphalt mix plant at the industrial scale (i.e. full scale).