This work presents an algorithm for calculating high temperature series expansions (HTSE) of Heisenberg spin models with spin $S=1/2$ in the thermodynamic limit. This algorithm accounts for the presence of a magnetic field. The paper begins with a comprehensive introduction to HTSE and then focuses on identifying the bottlenecks that limit the computation of higher order coefficients. https://www.spidertattooz.com/Fanimation-MAD8514-TriAire-52-Indoor-Outdoor-Ceiling-Fan/