We report on the acceleration of ion beams from ultrathin diamondlike carbon foils of thickness 50, 30, and 10 nm irradiated by ultrahigh contrast laser pulses at intensities of approximately 7 x 10;{19} W/cm;{2}. An unprecedented maximum energy of 185 MeV (15 MeV/u) for fully ionized carbon atoms is observed at the optimum thickness of 30 nm. The enhanced acceleration is attributed to self-induced transparency, leading to strong volumetric heating of the classically overdense electron population in the bulk of the target. Our experimental results are supported by both particle-in-cell (PIC) simulations and an analytical model.