In order to study the coupling fluid and thermal problems of the local winding in oil-immersed power transformers, the least-squares finite element method (LSFEM) and upwind finite element method (UFEM) are adopted, respectively, to calculate the fluid and thermal field in the oil duct. When solving the coupling problem by sequential iterations, the effect of temperature on the material property and the loss density of the windings should be taken into account. In order to improve the computation efficiency for the coupling fields, an algorithm, which adopts two techniques, the dimensionless LSFEM and the combination of Jacobi preconditioned conjugate gradient method (JPCGM) and the two-side equilibration method (TSEM), is proposed in this paper. To validate the efficiency of the proposed algorithm, a local winding model of a transformer is built and the fluid field is computed by the conventional LSFEM, dimensionless LSFEM, and the Fluent software. While the fluid and thermal computation results of the local winding model of a transformer obtained by the two LSFEMs are basically consistent with those of the Fluent software, the stiffness matrix, which is formed by the dimensionless scheme of LSFEM and preconditioned by the JPCGM and TSEM, has a smaller condition number and a faster convergence rate of the equations. Thus, it demonstrates a broader applicability.