We present a novel setup to measure the transverse magneto-optical Kerr effect in the extreme ultraviolet spectral range based on a fiber laser amplifier system with a repetition rate between 100 and 300 kHz, which we use to measure element-resolved demagnetization dynamics. The setup is equipped with a strong electromagnet and a cryostat, allowing measurements between 10 and 420 K using magnetic fields up to 0.86 T. The performance of our setup is demonstrated by a set of temperature- and time-dependent magnetization measurements with elemental resolution.