The heat capacity, Cp, of microcrystalline and large or single crystal ice was measured from 270 to 272.6 K and the effect of the heat input (required before measuring the increase in temperature) on the measured Cp investigated. The measured Cp of microcrystalline solids was much higher than that of large and single crystal solids and increased further with increase in the heat input. At 271.16 K, the measured Cp was independent of the heat input, but for higher temperatures, it increased nonlinearly with the heat input. These effects are caused by the increase in the volume fraction of intergranular water in impurity free ice with increase in both its temperature and the heat input. A significant fraction of the heat used for Cp measurement is consumed in melting ice at grain junctions which does not raise the temperature. Thus, the measured Cp appears to be much greater than the true value. Quantitative analysis of the data yielded results which agree reasonably well with the prediction of a theory given in J. Chem. Phys. 100, 4548 (1994).