This work focuses on the magnetocaloric effect (MCE) in the temperature range of 77 ~20 K, which is required for magnetocaloric liquefaction of hydrogen pre-cooled by liquid nitrogen. Heavy rare-earth intermetallics compounds exhibit two distinguished features in this temperature range, both maximum magnetic and adiabatic temperature changes (ΔS T and ΔT ad ) increase with decreasing Curie temperatures (T C ) and a giant maximum ΔS T and ΔT ad in the vicinity of 20 K is observed. With heavy rare-earth Laves phases RAl 2 and RNi 2 as examples, a mean-field approach is developed, confirming the $T_C^{ - 2/3}$ linear relation and rationalizing these features. In a next step, inspired by the sharply increasing trend of MCE near 20 K, we tuned T C of the light rare-earth Laves phases RAl 2 to the hydrogen condensation point. Successfully, a light rare-earth intermetallic series covering the full temperature range required by magnetocaloric hydrogen liquefaction is achieved.