We demonstrate multiwatt cw output power from an optically pumped quantum-dot semiconductor disk laser. Continuous-wave output power of 4.35 W with 22% slope efficiency was demonstrated at a center wavelength of 1,032 nm. This represents an increase in power of 15 times and an increase in slope efficiency of 10 times from the previously published results using Stranski-Krastanow grown quantum dots. An intracavity diamond heat spreader was used for thermal management. The maximum output power was limited by the available pump power, and no sign of thermal rollover was observed.