Slow granular flows play an important role in industries ranging from food to pharmaceuticals to ceramics, and this subject has received much recent attention in the literature. In contrast, heat transfer in even the simplest particle flows is poorly understood. In granular flows, conductivity depends strongly on the micro-structure of the bulk material: therefore, the particle mixing/segregation (i.e., "convective" heat transfer) will dramatically impact the total heat flow in the granular material. In this work, a multi-scale, multi-physics modeling technique – Thermal Particle Dynamics (TPD) – is used to examine how transient heat transfer and particle mixing interplay in rotating tumblers. We study the effects of tumbler cross section shape, and operation parameters – rotation rate and tumbler filling level – in the heating rate of the granular material. We present/compare temperature profiles and mixing patterns for equivalent granular systems. Our TPD simulation results are used to demonstrate that the rate of mixing is critical to the heat transfer rate in the granular material.