Two superconductors coupled by a weak link support an equilibrium Josephson electrical current that depends on the phase difference phi between the superconducting condensates(1). Yet, when a temperature gradient is imposed across the junction, the Josephson effect manifests itself through a coherent component of the heat current that flows opposite to the thermal gradient for vertical bar phi vertical bar < pi/2 (refs 2-4). The direction of both the Josephson charge and heat currents can be inverted by adding a pi shift to phi. In the static electrical case, this effect has been obtained in a few systems, for example via a ferromagnetic coupling(5,6) or a non-equilibrium distribution in the weak link(7). These structures opened new possibilities for superconducting quantum logic(6,8) and ultralow-power super-conducting computers(9). Here, we report the first experimental realization of a thermal Josephson junction whose phase bias can be controlled from 0 to pi. This is obtained thanks to a super-conducting quantum interferometer that allows full control of the direction of the coherent energy transfer through the junction(10). This possibility, in conjunction with the completely superconducting nature of our system, provides temperature modulations with an unprecedented amplitude of similar to 100 mK and transfer coefficients exceeding 1 K per flux quantum at 25 mK. Then, this quantum structure represents a fundamental step towards the realization of caloritronic logic components such as thermal transistors, switches and memory devices(10,11). These elements, combined with heat inter-ferometers(3,4,12) and diodes(13,14), would complete the thermal conversion of the most important phase-coherent electronic devices and benefit cryogenic microcircuits requiring energy management, such as quantum computing architectures and radiation sensors.