This work is devoted to the two-dimensional (2D) numerical simulation of heat and fluid flow by granular mixing in a horizontally rotating kiln. The heat and fluid flow in the gas phase are solved directly using a fixed Eulerian grid. At the same time, the particle dynamics and their collisions are solved on a Lagrangian grid. The no-slip boundary condition on the particle surface is implemented using the fictitious boundary method. The heat transfer inside the particles is calculated utilising two models: the first is the direct solution of the energy conservation equation in Lagrangian and Eulerian space and the second is the so-called linear model, which assumes a homogeneous distribution of the temperature inside each particle. Numerical simulations showed that if the thermal diffusivity of the gas phase significantly exceeds the same parameter of the particles, the linear model over-predicts the heating rate of the particles. The analysis of the time-averaged flow field inside the kiln showed that in the gas phase a double vortex structure is formed which increases the convective heat transfer in the upper part of the particulate bed. The influence of the particle size, the angular velocity of the drum and the fluid on the heating rates of particles is studied and discussed.