This work is focused on topology optimization of heat transfer in two dimensional problems (2D). Its aim was to perform simulations on different MATLAB routines for the topological optimization of pure heat conduction, trying to emulate the traditional tree-like optimized conductive pathway commonly seen in literature. Firstly, we discuss the 99-line educational algorithm created by Ole Sigmund and known till this day as the access point for the learning and implementing of topology optimization for compliance minimization of statically loaded structures. Afterwards, this script was altered to adapt it to topology optimization for heat conduction in isotropic and homogeneous domains. To further illustrate the algorithm s functioning, different optimizations were conducted by altering specific parameters, such as the total number of mesh elements and the filter s size. General applications and limitations of this method were discussed. To conclude the work, PolyTop, an efficient MATLAB code for structural topology optimization using unstructured meshes with polygonal finite elements were introduced and discussed, followed by its alteration for single physics topology optimization of heat transfer. Also, as part of the validation process, different initial conditions were simulated and resulting optimized branched structures compared with topologies obtained with Sigmund s adapted 99-line.