We study the evolution of dynamic fluctuations averaged over different space lengths and time scales to characterize spatially and temporally heterogeneous behavior of TIP4P/2005 water in liquid and supercooled states. Analyzing a 250 000 molecules simulated system, we provide evidence of the existence, upon supercooling, of a significant enhancement of spatially localized dynamic fluctuations stemming from regions of correlated mobile molecules. We show that both the magnitude of the departure from the value expected for the system-size dependence of an uncorrelated system and the system size at which such a trivial regime is finally recovered clearly increase upon supercooling. This provides a means to estimate an upper limit to the maximum length scale of influence of the regions of correlated mobile molecules. Notably, such an upper limit grows two orders of magnitude on cooling, reaching a value corresponding to a few thousand molecules at the lowest investigated temperature.