•A symplectic analytical approach is proposed to study the thermal-metallurgical coupling problems.•The symplectic analytical solution of three-dimensional temperature field is derived directly.•An alternating algorithm is designed to realize the nonlinear thermal-metallurgical coupling calculation.•The symplectic approach considers both quantization mechanism and computational efficiency.•The temperature and microstructure evolution during the coil cooling process are precisely calculated. The cooling process of hot-rolled coil directly affects the mechanical and metallurgical properties of the final product. The non-uniform behavior of temperature and microstructure can easily result in sufficient residual stress to induce subsequent cutting deformation. Therefore, the focus of this study is to analyze the thermal-metallurgical coupling problem during the cooling process of hot-rolled coil. Unlike before, a symplectic analytical approach is proposed to calculate the temperature and microstructure evolution of hot-rolled coil. Firstly, the hot-rolled coil is discretized to convert the three-dimensional heat transfer problem in cylindrical coordinate system to cartesian coordinate system. Then, the traditional heat transfer model is introduced into the symplectic Hamiltonian system and the symplectic superposition method is employed to handle complex cooling boundary conditions. The symplectic analytical solution of the three-dimensional temperature field is obtained through rigorous derivation without any assumptions or predetermined solution forms. Meanwhile, an alternating algorithm is designed between the heat transfer model and the phase transformation dynamics model to realize the coupling process. Moreover, a high-precision finite element model verified by the measured data is established. The symplectic analytical solution of coil temperature and microstructure during the cooling process is in good agreement with the finite element solution. Finally, the symplectic approach has been proven to enable quantitative mathematical analysis of the coupling mechanism of thermal-metallurgical processes.