Saturn's satellite Phoebe is the best-characterized representative of large outer Solar System planetesimals, thanks to the close flyby by the Cassini spacecraft in June 2004. We explore the information contained in Phoebe's physical properties, density and shape, which are significantly different from those of other icy objects in its size range. Phoebe's higher density has been interpreted as evidence that it was captured, probably from the proto-Kuiper-Belt. First, we demonstrate that Phoebe's shape is globally relaxed and consistent with a spheroid in hydrostatic equilibrium with its rotation period. This distinguishes the satellite from 'rubble-piles' that are thought to result from the disruption of larger proto-satellites. We numerically model the geophysical evolution of Phoebe, accounting for the feedback between porosity and thermal state. We compare thermal evolution models for different assumptions on the formation of Phoebe, in particular the state of its water, amorphous or crystalline. We track the evolution of porosity and thermal conductivity as well as the destabilization of amorphous ice or clathrate hydrates. While rubble-piles may never reach temperatures suitable for porous ice to creep and relax, we argue that Phoebe's shape could have relaxed due to heat from the decay of 26Al, provided that this object formed less than 3 Myr after the production of the calcium-aluminum inclusions. This is consistent with the idea that Phoebe could be an exemplar of planetesimals that formed in the transneptunian region and later accreted onto outer planet satellites, either during the satellite's formation stage, or still later, during the late heavy bombardment.