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Nonisothermal reaction-diffusion systems control the behavior of many transport and rate processes in physical, chemical and biological systems, such as pattern formation and chemical pumps. Considerable work has been published on mathematically coupled nonlinear differential equations by neglecting thermodynamic coupling between a chemical reaction and transport processes of mass and heat. This study presents the modeling of thermodynamically coupled system of a simple elementary chemical reaction with molecular heat and mass transport. 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 or reaction affinity. The modeling is based on the linear nonequilibrium thermodynamics approach by assuming that the system is in the vicinity of global equilibrium. The modeling equations lead to unique definitions of cross-coefficients between a chemical reaction and heat and mass flows in terms of kinetic parameters, transport coefficients and degrees of coupling. These newly defined parameters need to be determined to describe some coupled reaction-transport systems. Some methodologies are suggested for the determination of the parameters and some representative numerical solutions for coupled reaction-transport systems are presented.