We report on the optical cooling of a 7.5%Yb:LiYF4 crystal down to 125 K in a multi-pass Herriott absorption cell, coupled via a single mode polarization maintaining optical fiber to the laser source. This configuration, never exploited before, is more practical for potential applications, in particular for spaceborne cryogenics setups. Moreover, the temperature reached is exactly the one needed in many setup embarked in small and medium satellites. We evaluate the heat load on the crystal at the minimum attainable temperature, which is comparable to state of the art systems.