We have observed that the infrared-active stretching modes of hydrogen in device-quality a-Si:H films are redshifted as the temperature increases. Over the range of temperatures studied, 100-600 K, the shift is approximately linear with temperature, 0.035 cm-1 K-1, and shows a totally reversible behavior. We have established that changes in the polarization of the material, via changes of the dielectric constant with temperature, can lead to small shifts, but cannot explain the magnitude of the experimentally observed effect. We compare our results with a similar observation made on well defined hydrogen-terminated Si surfaces. In that case, the shift was attributed to the coupling of the hydrogen stretching motion with lower-frequency phonons. We propose that an analogous coupling mechanism is present in the a-Si:H structure.