The BOD5-DO ( Biochemical Oxygen Demand in five days and Dissolved Oxygen) are important indexes that reflect the organic pollution extent of water，but the variation of the indexes is closely related with water temperature． The study on the coupled mathematical model reflecting the BOD5-DO with temperature is the key to reveal the mechanism of the migration and distribution of BOD5-DO in the water． The authors presented 1-D mathematical model for the three variables in vertical direction，and gave accurate solution for the equations under steady state，the relation among the variables and the method for solving BOD5-DO concentrations at different depth and temperature．