Recycling aged asphalt pavements into new asphalt pavements is a common practice in the pavement industry. The process involves adding the reclaimed asphalt pavement (RAP) into a superheated asphalt mixing drum, where the binder contained within the RAP is expected to melt and be incorporated into the new hot-mix asphalt. Since the RAP is added part way through the mixing process, the amount of time spent inside the mixing drum is short and possibly insufficient for the RAP binder to melt and mix with the new asphalt binder. To address this issue, a numerical model is developed using the thermal properties of asphalt materials to investigate the melting potential of the RAP inside an asphalt mixing drum. Through a dimensionless analysis, the proposed model allows for the practice-ready calculation of the minimum time needed for any spherical particle to heat to a desired temperature given the initial temperature, ambient temperature, thermal diffusivity, and particle radius. Using the resulting equation, it is shown that there may be cases in which the RAP is not sufficiently heated inside an asphalt mixing drum.