The unlit side of the dense B ring of Saturn does not receive direct sunlight. Yet it cools down as the Sun sets on the ring from solstice to equinox. A multi-scale thermal model that treats the heat transfer through a packed ensemble of particles is built to study the orbital and seasonal temperature variations of both lit and unlit sides of this opaque ring. Heat transfer by radiation, conduction or through contacts are considered both at the ring and the particles scale. A statistical approach shows that three simple constraints, such as the heat diffusion time through the ring, the current estimates on its thermal inertia and its optical depth, yield important constraints on its thickness, its filling factor and on particle properties such as their thermal inertia, porosity or size. The B ring is probably a few-meters-thick, with a filling factor D below 0.25, made of a population of porous but still conductive particles. Its thickness is compatible with a surface mass density ranging between 50 and 75 g/cm2 in its densest part.