We present an analytical solution for the thermal transport in fluid-particle systems that include a spatially and temporally constant volumetric heat source. Our solution enables the rapid calculation of temperature profiles in systems undergoing chemical reactions or phase change phenomena. Also, we propose a map that helps in deciding in which situations the simple solution of Schumann (1929) [15] is enough to calculate fluid and particle temperatures. (C) 2017 Elsevier B.V. All rights reserved.