This article is part of a two paper series presenting a development in the methodology for the calculation of response functions for geothermal fields with arbitrarly oriented boreholes. In the method utilized, boreholes are represented as sets of stacked line sources and the borehole temperatures are calculated by means of a superposition procedure. This particular paper is focused on the efficient computation of the building block of this approach, which is the non dimensional mean temperature response (g) over tilde (t) along a finite line due to a step heat injection along a second finite line, where the lines are arbitrarily oriented. The speed in computing this function is critical for the applicability of the method. The solution proposed to achieve the required performance is a hybrid approach involving analytical, numerical and implementation aspects: an analytical procedure to simplify the expression of (g) over tilde (t) was developed, the resulting problem was solved with a tailored numerical method, and the algorithm was implemented using a high-performing programming language. Each of these aspects showed to have a great impact from a performance perspective. The performance achieved in the calculation of (g) over tilde (t) enables the integration of this method within the scheme utilized for g-functions calculation. (c) 2015 Elsevier Ltd. All rights reserved.