Solutions of glycerol and water of intermediate concentration – about glycerol 50% or 60% (w/w) – vitrify homogenously if cooled fast enough. On heating, however, water's crystallization tendency prevails and ice grows at the expense of the water contents of the homogeneous glycerol aqueous matrix. It must be noted, though, that ice formation stops well before a pure glycerol phase is attained and, therefore, the two phases that remain in the end are (i) a pure ice (water) phase and (ii) a glycerol-rich phase known as the maximally freeze-concentrated solution, MFCS for short. Water's spontaneous crystallization on heating takes place at temperatures appreciably lower than the corresponding temperatures at the equilibrium binary phase diagram and has been observed to lead to the formation of a novel two-dimensionally ordered structure of ice – 2D-Ice – as characterized through its neutron diffraction patterns. We report here the results of a recent calorimetric characterization of 2D-Ice and the MFCS obtained from a glycerol 55% (w/w) aqueous solution. Measurements using an adiabatic calorimeter allowed us to evaluate the heat capacity and concentration of the MFCS – evaluated to be glycerol 74.3% – and to establish that, on average, the heat capacity of 2D-Ice is 1.3% larger than that of ordinary hexagonal (Ice Ih) between T = 6 K and T = 15 K (see Fig. 3).