Transiting extrasolar planets are key objects in the study of the formation , migration , and evolution of planetary systems [ ] . In particular , the exploration of the atmospheres of giant planets , through transmission spectroscopy or direct imaging , has revealed a large diversity in their chemical composition and physical properties [ ] . Studying these giant planets allows one to test the global climate models [ ] that are used for the Earth and other solar system planets . However , these studies are mostly limited either to highly-irradiated transiting giant planets or directly-imaged giant planets at large separations . Here we report the physical characterisation of the planets in a bright multi-planetary system ( HIP41378 ) in which the outer planet , HIP41378 f is a Saturn-sized planet ( 9.2 \pm 0.1 R _ { \oplus } ) with an anomalously low density of 0.09 \pm 0.02 g cm ^ { -3 } that is not yet understood . Its equilibrium temperature is about 300 K. Therefore , it represents a planet with a mild temperature , in between the hot Jupiters and the colder giant planets of the Solar System . It opens a new window for atmospheric characterisation of giant exoplanets with a moderate irradiation , with the next-generation space telescopes such as JWST [ ] and ARIEL [ ] as well as the extremely-large ground-based telescopes . HIP41378 f is thus an important laboratory to understand the effect of the irradiation on the physical properties and chemical composition of the atmosphere of planets .