The influences of temperature on the SFG spectra of Langmuir-Blodgett films of cadmium stearate, ferric stearate, stearic acid and octadecamide are reported. Upon cooling, all films display reversible discontinuous shifts of ~8 cm^-1 in the r⁺, r^- and r_fermi modes of the terminal methyl groups at ~150 K. Reversible changes in the relative intensities of these methyl group peaks, most pronounced in the PPP spectra, are also observed and attributed to a change in symmetry of the methyl group. The onset of new spectral features at higher frequency is attributed to the observation of ordered water molecules contained within the films. The correlation between the onset of the ordered water features and the onset of the reversible, discontinuous, spectroscopic changes of the amphiphiles argues for a causal connection and allows us to propose a model to explain this behavior. Monolayer films of stearic acid and octadecamide display reversible, temperature dependent activity of methylene modes upon exposure to vacuum. Monolayer films of cadmium stearate and ferric stearate do not display this methylene activity upon exposure to vacuum, suggesting that this behavior may be linked to solvation of the amphiphile's head group. These observations imply that water plays a key role in the stability and structure of LB supported monolayers, and have important implications to those interested in low temperature (cryogenic) effects of biological systems. In addition, these observations raise larger questions regarding the low temperature phase behavior of water at interfaces.