To increase the chances of recovery for patients with a fatty liver or diabetes, it is necessary to ensure an adequate supply of certain substances such as oxygen to the liver. This is due to the fact that these substances are required in biochemical reactions to maintain the liver function and to trigger self curing processes. Determining the volumetric flow rate and blood pressures in these vessels, we use a modeling approach that is based on a coupled one-dimensional partial and ordinary differential equations (1D-0D coupled blood flow models). It is combined with models for heat transfer in biological tissue. This is motivated by the fact that the volumetric flow rate of blood can be increased for a certain period of time by applying hot or cold stimuli. If a patient suffers from cardiac insufficiency, small heart chambers or a lack of oxygen in the blood, the resulting reduced supply of the liver by oxygen can be increased by means of thermotherapy. An important factor for the precise determination of flow rates in networks composed of the main systemic arteries is a precise knowledge of the heart rate. For this purpose, an interface to an in-ear sensor is established, transferring measured heart beats and oxygen saturations in blood to the simulation program for heat transfer and blood flow. Since the heat transfer in tissue is a slow diffusion dominated process compared to blood flow in larger arteries, a multi-scale problem with respect to time is resulting. In this talk, we present some strategies and first insights related to the coupling of blood flow and heat transfer. Moreover, some simulation results are shown. Finally, we discuss some ideas on how methods from machine learning can help us to compute quantities of interest in a fast way.