Experiments investigating the properties of deeply supercooled liquid water are needed to develop a comprehensive understanding of water's anomalous properties. One approach involves transiently heating nanoscale water films into the supercooled region for several nanoseconds at a time and then interrogating the water films after they have quenched to cryogenic temperatures. To relate the results obtained with this approach to other experiments and simulations on supercooled water, it is important to understand how closely the quenched structure tracks the (metastable) equilibrium structure of water as a function of the transient heating temperature. A key step involves quantifying the extent to which water that is transiently heated to ambient temperatures [hyperquenched water (HQW)] subsequently relaxes toward the structure of low-density amorphous (LDA) ice as it cools. We analyzed the infrared reflection-absorption spectra of LDA, HQW, and crystalline ice films to determine their complex indices of refraction. With this information, we estimate that HQW retains ∼50%-60% of a structural motif characteristic of water at high temperatures with the balance comprised of a low-temperature motif. This result, along with results from x-ray diffraction experiments on water and amorphous ices, allows one to quantify the fraction of the high-temperature motif at approximately zero pressure as a function of temperature from 150 to 350K.