A -p--linear dimensionless average fluid temperature was proposed to estimate borehole thermal resistance. A -p--linear dimensionless fluid temperature and the -p--linear dimensionless average fluid temperature were introduced, and the -p--linear dimensionless fluid temperature was compared with theoretical dimensionless fluid temperature calculated by quasi-three-dimensional model for both single and double U-tubes. Results show that the -p--linear dimensionless temperatures with parameters -p-→0 and -p-= -1/2 are respectively in good agreement with the theoretical dimensionless fluid temperatures of single and double U-tubes. Therefore, the dimensionless logarithmic mean temperature for -p-→0 and the dimensionless geometric mean temperature for -p-= -1/2 should respectively be adopted to reasonably estimate the thermal resistance of single and double U-tube boreholes.