mostly investigated in experiments with ultra-cold atoms and single atomic traps. Experiments with superconducting qubits have also been carried out and heat transport and heat rectification has been studied in two terminal devices. The structures with three independent terminals offer additional opportunities for realization of heat transistors, heat switches, on-chip masers and even more complicated devices. Here we report an experimental realization of a three-terminal photonic heat transport device based on a superconducting quantum circuit. Its central element is a flux qubit made of a superconducting loop containing three Josephson junctions, which is connected to three resonators terminated by resistors. By heating one of the resistors and monitoring the temperatures of the other two, we determine photonic heat currents in the system and demonstrate their tunability by magnetic field at the level of 1 aW. We determine system parameters by performing microwave transmission measurements on a separate nominally identical sample and, in this way, demonstrate clear correlation between the level splitting of the qubit and the heat currents flowing through it. Our experiment is an important step in the development of on-chip quantum heat transport devices. On the one hand, such devices are of great interest for fundamental science because they allow one to investigate the effect of quantum interference and entanglement on the transport of heat. On the other hand, they also have great practical importance for the rapidly developing field of quantum computing, in which management of heat generated by qubits is a problem.