The estimation of thermal conductivity (k) by Ångström's method is well known and a popular alternative to the existing ASTM standards because it allows for an easier setup due to the model's simpler boundary conditions. The shortcomings of this approach are that only two temperature locations are used, making it highly sensitive to temperature sensor placement. Moreover, the approach uses only the first term in the Fourier series of the solution causing inaccuracies in the model. An alternative multi-point model presented in this study corrects both of these problems. The study uses the new multi-point method to estimate k and compares the accuracy to the Ångström's method. The benefit of Ångström's method and other existing steady state harmonic methods is that they manipulate the solution so that k decouples from the unknown heat transfer coefficient (h). The multi-point model uses parameter estimation to estimate both h and k simultaneously. In this study, the accuracy of the k estimation was examined for three materials with a k range of 15–400 W/mK at three different oscillation periods: 50, 100, and 200 s. The results show that the proposed new method is more robust than the previous methods, with the same order of accuracy as existing ASTM standards.