We study by Monte Carlo simulations and mean field calculations the specific heat $C_P$ of a cell model that reproduces known properties of water. In the supercooled regime we find \emph{two} $C_P$ maxima that are strikingly similar to very recent experimental results. We show that the maximum at higher temperature is associated with the fluctuations of hydrogen bond formation and that the second maximum at lower temperature is associated with the cooperativity of the hydrogen bonds. If this cooperativity is not taken into account, the lower temperature maximum disappears. Our finding offers a \emph{thermodynamic} interpretation for the two maxima in $C_P$.