Considerable work published on chemical reaction-diffusion systems investigates mainly mathematically coupled nonlinear differential equations. This study presents the modeling of a simple elementary chemical reaction with thermodynamically and mathematically coupled heat and mass transport with external mass and heat transfer resistances. The thermodynamic coupling refers that a flow occurs without or against its primary thermodynamic driving force, which may be a gradient of temperature or chemical potential. The modeling is based on the linear nonequilibrium thermodynamics approach and phenomenological equations by assuming that the system is in the vicinity of global equilibrium. This approach does not need detailed coupling mechanisms. The modeling equations contain the cross coefficients controlling the coupling between heat and mass flows in terms of transport coefficients and surface conditions. These coefficients need to be determined for rigorous analysis of chemical reaction systems with thermodynamically coupled transport phenomena. Some representative numerical solutions of the modeling equations are presented to display the effect of coupling on concentration and temperatures in time and space for simple exothermic catalytic reactions.