We report AC heat capacity measurements of the icosahedral phase of Al₆CuLi₃ between 0.25 and 2.7 K. These Camples are cast in ingots and are composed of interdendritic regions of quasi-crystal phase (0.1 mm × 3.0 mm) interlaced with an Al and R-phase solid solution (13% of sample). Heat capacity and resistivity measurements both indicate a superconducting transition of about 1.4 K for these samples. The relative contribution from the icosahedral phase and the aluminum to the properties of the sample are discussed.