A search for resonant absorption of solar axions by 169Tm nuclei was carried out. A newly developed approach involving low-background cryogenic bolometer based on Tm3Al5O12 crystal was used that allowed for significant improvement of sensitivity in comparison with previous 169Tm based experiments. Themeasurements performed with 8.18 g crystal during 6.6 days exposure yielded the following limits on axion coupli...