The U-shaped ground heat exchanger (UGHE) offers an effective solution for building heating and cooling purposes. In the practical applications of vertical UGHEs, the borehole wall temperature varies along the borehole depth due to the uneven initial ground temperature and transient heat transfer process. The assumption of a uniform temperature along the borehole wall in the existing quasi-3D model of UGHE causes a non-negligible error in the calculation of fluid temperature, especially for the cases of shallow-medium boreholes. Thus, two new analytical models are established to calculate the fluid temperatures for the single U-shaped GHE (1-UGHE) and double U-shaped GHE (2-UGHE), considering the depth-dependent borehole wall temperatures. The convolution theorem is employed to solve the mathematical problem of the nonlinear condition on the borehole wall, and the Laplace transformation is used for getting the final temperature expressions. The new analytical models are compared and verified by the on-site experiments. The results show that the two models exhibit promising prediction accuracies and similar variation trends in fluid temperatures. Then, parametrical and economical analyses for 1−/2- UGHEs have been carried out. Finally, the geographical thermal potentials of 1−/2- UGHEs across China have been comparatively investigated and the corresponding thermal map-based application potential recommendations have been given.