To quickly and accurately compute the borehole fluid and ground temperature, a new thermal response factors (referred as δ-function) was proposed to calculate the ground temperature response of bore field to a unit rectangular heat pulse. The proposed model is based on the existing models for the long δ-term simulation of vertical heat exchanger. In this paper, the δ-function was combined with the fast Fourier transform to improve the computation speed of the δ-function. Then, the response factor and algorithm were compared with the δ- function in terms of accuracy and computation time. The results show that when combined with the fast Fourier transform, the g-function not only has the same precision with that of the g-function, but also has significantly faster computation speed than that of the g-function. It only spends shorter than 90 seconds to complete the 30 year hourly simulation of a 5×8 bore field.