We present a femtosecond laser system delivering up to 100 W of average power at 343 nm. The laser system employs an Yb-based femtosecond fiber laser and subsequent second- and third-harmonic generation in beta barium borate (BBO) crystals. Thermal gradients within these BBO crystals are mitigated by sapphire heat spreaders directly bonded to the front and back surface of the crystals. Thus a nearly diffraction-limited beam quality (M²<1.4) is achieved despite the high thermal load to the nonlinear crystals. This laser source is expected to push many industrial and scientific applications in the future.