Conduction transfer functions (CTF) are commonly used in the building services to quickly estimate hourly conduction heat loads through multilayered walls without resorting to expensive, time-consuming solutions of the heat equation. It is essential for any software developed for this purpose to be able to simulate walls of varying weight with a high degree of accuracy. A robust algorithm for computing CTF coefficients and thermal response factors based on power series expansions of solutions of the governing equations in the complex s-domain is presented and validated. These series expansions are used to to construct Pad\'e approximants of the system's transfer functions, which greatly simplifies the inversion of the solution from the complex domain to the time domain, and allows for an easy recovery of a time series representation via the Z-transform. The algorithm is also implemented in an open-source C++ code. Its performance is validated with respect to exact theoretical frequency characteristics and its results are compared with data generated by previously established methods for computing CTF coefficients / response factors.