The NA60 experiment at the CERN SPS has studied low-mass dimuon production in 158A GeV In-In collisions. An excess of pairs above the known meson decays has been reported before. We now present precision results on the associated transverse momentum spectra. The slope parameter Teff extracted from the spectra rises with dimuon mass up to the rho, followed by a sudden decline above. While the initial rise is consistent with the expectations for radial flow of a hadronic decay source, the decline signals a transition to an emission source with much smaller flow. This may well represent the first direct evidence for thermal radiation of partonic origin in nuclear collisions.