We present the first self-mode-locked optically pumped quantum-dot semiconductor disk laser. Our mode-locked device emits sub-picosecond pulses at a wavelength of 1040 nm and features a record peak power of 460 W at a repetition rate of 1.5 GHz. In this work, we also investigate the temperature dependence of the pulse duration as well as the time-bandwidth product for stable mode locking.