Based on a modelling technique to calculate the thermal influence of a single vessel segment, a combination of segments representing a vessel tree is presented. At segment junctions the blood temperature is passed with a correction for a single vessel artefact. Blood leaving the modelled arterial vessel network at a junction or at the end of a terminal branch need not be equilibrated with the local surrounding tissue temperature. The thermal effect of this equilibration process can be taken into account using the 'sink set'. Blood entering a venous vessel tree is given an inflow temperature based on the tissue temperatures in the 'sample set'. With these sets we model the thermal impact of the vasculature too small to be taken into account discretely. The formation of the sink/sample sets is subject of current research; to show the capabilities of the presented method we present a minimal simulation collection with cube-shaped sets in combination with limited vasculature. The results of using the entire simulation volume as sink and sample sets for all the terminal branches matches the reference temperature profile best.