A fundamental understanding of the unusual properties of water remains elusive because of the limited data at the temperatures and pressures needed to decide among competing theories. We investigated the structural transformations of transiently heated supercooled water films, which evolved for several nanoseconds per pulse during fast laser heating before quenching to 70 kelvin (K). Water's structure relaxed from its initial configuration to a steady-state configuration before appreciable crystallization. Over the full temperature range investigated, all structural changes were reversible and reproducible by a linear combination of high- and low-temperature structural motifs. The fraction of the liquid with the high-temperature motif decreased rapidly as the temperature decreased from 245 to 190 K, consistent with the predictions of two-state "mixture" models for supercooled water in the supercritical regime.