Proposals for next-generation gravitational wave observatories include cryogenically cooled 200 kg test mass mirrors suspended from pendulums and made of a crystalline material such as crystalline silicon. During operation of the observatories, these mirrors undergo heating due to the absorption of laser radiation of up to a watt. Low noise cooling techniques need to be developed. Low-pressure helium exchange gas at 5 K might contribute to the challenging task. Here, we report the measurement of the helium accommodation coefficient α(11 K < T < 30 K), which is the probability that a helium atom thermalises with a surface at a given temperature when reflected from it. We find α(T) > 0.7 for temperatures < 20 K, which increases the cooling power compared to recently used assumptions. The idea of free molecular flow helium gas cooling is thus supported and might find application in some observatory concepts.