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Active matter consists of particles which can move because of local consumption of energy. Think about bacteria like E. Coli, which seem to run for some time, with a typical propulsion speed, after which they tumble to randomly change the orientation of their movement. Their running and tumbling is fueled by food and their "health" is visible from their "activity". In the same way we can speak about active matter when studying general materials with the intrinsic ability to generate movement, or so called self-propulsion. This thesis is not directly concerned with collective behavior of those active particles. We focus on that they do to a passive probe immersed in their midst. In other words we insert a slower, perhaps bigger but certainly "dead" and passive probe in a bath of active particles. We can imagine putting a rod with one end in a heap of ants. The other end is inserted in another bath, possibly passive. This thesis is studying the heat flowing through that rod. In what sense is there really a current of energy transported between the edges of that rod? The rod is modeling by a chain of oscillators, like springs and beads as passive probes. One active bath affects one end of the rod. We have the run-and-tumble particles interacting with the outermost probes. The rod is modelled with Newtonian classical dynamics and energy is locally conserved. That allows indeed to define a heat current. Note however that there is no direct distinction between the energies of the active baths; they are at the same temperature as their kinetic energy is approximately equal. And yet, the current flows and increases with the difference of activity between the baths. That is a fascinating fact, which here first established. As method we used computer simulations, an indispensable tool for research in non-equilibrium physics. Lots of the work and effort went to getting the algorithm to work well, which moreover allows visualizations as common for Python.