The yield of muon pairs in the invariant mass region 1<M<2.5 GeV/c 2 produced in heavy-ion collisions significantly exceeds the sum of the two expected contributions, Drell-Yan dimuons and muon pairs from the decays of D meson pairs. These sources properly account for the dimuons produced in proton-nucleus collisions. In this paper, we show that dimuons are also produced in excess in 158 A∈GeV In-In collisions. We furthermore observe, by tagging the dimuon vertices, that this excess is not due to enhanced D meson production, but made of prompt muon pairs, as expected from a source of thermal dimuons specific to high-energy nucleus-nucleus collisions. The yield of this excess increases significantly from peripheral to central collisions, both with respect to the Drell-Yan yield and to the number of nucleons participating in the collisions. Furthermore, the transverse mass distributions of the excess dimuons are well described by an exponential function, with inverse slope values around 190 MeV. The values are independent of mass and significantly lower than those found at masses below 1 GeV/c 2, rising there up to 250 MeV due to radial flow. This suggests the emission source of thermal dimuons above 1 GeV/c 2 to be of largely partonic origin, when radial flow has not yet built up.