Recent stellar occultations have allowed accurate instantaneous size and apparent shape determinations of the large Kuiper belt object (50000) Quaoar and the detection of two rings with spatially variable optical depths. In this paper we present new visible range light curve data of Quaoar from the Kepler/K2 mission, and thermal light curves at 100 and 160um obtained with Herschel/PACS. The K2 data provide a single-peaked period of 8.88h, very close to the previously determined 8.84h, and it favours an asymmetric double- peaked light curve with a 17.76h period. We clearly detected a thermal light curve with relative amplitudes of ~10% at 100 and at 160um. A detailed thermophysical modelling of the system shows that the measurements can be best fit with a triaxial ellipsoid shape, a volume-equivalent diameter of 1090km, and axis ratios of a/b=1.19 and b/c=1.16. This shape matches the published occultation shape, as well as visual and thermal light curve data. The radiometric size uncertainty remains relatively large (+/-40km) as the ring and satellite contributions to the system-integrated flux densities are unknown. In the less likely case of negligible ring or satellite contributions, Quaoar would have a size above1100 km and a thermal inertia 10J/m2/K1/s1/2, notably higher than that of smaller Kuiper belt objects with similar albedo and colours. We find that Quaoar's density is in the range 1.67-1.77g/cm3 , significantly lower than previous estimates. This density value closely matches the relationship observed between the size and density of the largest Kuiper belt objects.