The heat capacity (C p ) and dilatation (α) of YB 12 and LuB 12 are studied. C p of the zone-melted YB 12 tricrystal is measured in the range 2.5-70 K, of the zone-melted LuB 12 single crystal in the range 0.6-70 K, and of the LuB 12 powder sample in the range 4.3-300 K; α of the zone-melted YB 12 tricrystal and LuB 12 single crystals is measured in the range 5-200 K. At low temperatures a negative thermal expansion (NTE) is revealed for both compounds: for YB 12 at 50-70 K, for LuB 12 at 10-20 K and 60-130 K. Their high-temperature NTE is a consequence of nearly non-interacting freely oscillating metal ions (Einstein oscillators) in cavities of a simple cubic rigid Debye lattice formed by B 12 cage units. The Einstein temperatures are ∼254 and ∼164 K, and the Debye temperatures are ∼1040 K and ∼1190 K for YB 12 and LuB 12 respectively. The LuB 12 low-temperature NTE is connected with an induced low-energy defect mode. The YB 12 superconducting transition has not been detected up to 2.5 K.