Ground-coupled heat pump (GCHP) system is one of the important renewable energy systems. Vertical ground heat exchanger (GHE) is the most expensive part of GCHP systems. Fast and accurate computation of fluid and ground temperatures is desired for the long-term prediction of GCHP performance and the optimal sizing of borehole fields. In this paper, a thermal response factors, delta-function is proposed for computing fluid and ground temperatures of borehole fields. delta-function is a non-dimensional ground temperature response and an accurate analytical solution of finite line source model to a unit rectangular heat pulse. Numerical computation of delta-function is quite fast for its small integral range. The accuracy of delta-function is validated by the simulation results of g-function. The comparative computations are conducted for the hourly simulation of various long periods by combining the g- and delta-functions with both time and spectral domain methods. It is found that the combination of g-function with fast Fourier transform (FFT) provides dramatically fast computing speed. Therefore, the computation approach of delta-function combined with FFT is the most suitable to quickly and accurately compute the fluid and ground temperatures in parameterized design and long-term simulation of vertical GHE and GCHP systems. (C) 2019 Elsevier Ltd. All rights reserved.