We devised a method to measure erosion in the micrometer range on actively cooled tungsten samples. The method is based on applying micrometer-sized markers onto the side faces of the samples using a focused ion beam. With this method we measured the erosion of tungsten samples exposed to a hydrogen beam with 6 % helium content. At 10.5 MW/m2 the samples were exposed to particle fluences between 2 ¡Á 1025 m?2 and 7 ¡Á 1025 m?2. Up to 630 pulses with a pulse duration of 30 s were employed. The actively cooled samples reach an equilibrium surface temperature which was varied from about 600 ¡ãC to 2000 ¡ãC. We find an amount of erosion which clearly exceeds the value computed from physical sputtering yields by roughly a factor of two. This is possibly correlated with the formation of a complex nanometer-sized morphology, which was observed for all temperatures.