Optimal design and operation of borehole fields require accurate prediction of the dynamic heat transfer in the ground. For large borehole systems, current simulation algorithms do not have the scaling properties to enable complex borehole network simulations with both fine source discretizations as well as fine time resolution. This paper is focused on the so-called “non-history dependent” method, a procedure for the acceleration of the time superposition process with promising properties that could be instrumental to improve on current scaling limitations. In this development, we considered the case of the point source and we derived an analytical expression for the scheme. The computation of the temperature involves the integration of an oscillatory function. A scheme for the numerical integration step of the algorithm based on integration techniques for oscillatory integrals is proposed. We study the computational complexity of the algorithm, which is linear in the number of time steps and in the number of integration points. Additionally, refining the discretizations used to perform the numerical integral leads to accuracy close to double precision. As a result, we conclude that the algorithm presents both favorable accuracy and performance features.