An Eulerian-Eulerian model for particle-laden flows is extended to a non-isothermal case. The characteristic form of the hyperbolic Eulerian system of equations, for both the carrier and particle phase, is derived and utilized to numerically solve the Eulerian-Eulerian model with a first order Godunov scheme. The derivation of the Eulerian-Eulerian model is presented, as well as the governing equations for the particles in the Lagrangian framework. The carrier phase model, decoupled from the particles, is verified with the 1D CLAWPACK Euler solver and the weighted essentially non-oscillatory (WENO-Z) particle-source-in-cell (PSIC) Eulerian-Lagrangian based solver for a classical shock tube problem. The Eulerian model equations for the particle phase are verified for a uniform flow that encounters a cloud of particles, with analytical formulations. The Eulerian-Eulerian model is then validated against the WENO-Z EL based solver for a subsonic flow case and a case where a running shock is inflicted on a cloud of particles.