Accurate simulations of the behavior of RF waves in hot, magnetized fusion plasmas have traditionally been computationally demanding due to the integro-differential character of the hot plasma wave equation. In this work a method is described that allows the integral in the hot-plasma wave equation to be rewritten as a set of differential operators by fitting a polynomial through the dielectric tensor components. This approach is applied to a one-dimensional simulation with typical profiles and plasma parameters for the JET fusion reactor. The accuracy and computational time are compared with an all-orders model and a truncated Finite Larmor Radius model. It is shown that the proposed method can be used to achieve accuracies previously only obtained with extremely heavy all-orders models like the two-dimensional AORSA code, but at significantly reduced computational costs. The MATLAB code that has been developed in this work is available under the GPLv3 licence.