Observations of thermally driven transverse vibration of a photonic crystal waveguide (PCW) are reported. The PCW consists of two parallel nanobeams whose width is modulated symmetrically with a spatial period of 370 nm about a 240-nm vacuum gap between the beams. The resulting dielectric structure has a band gap (i.e., a photonic crystal stop band) with band edges in the near infrared that provide a regime for transduction of nanobeam motion to phase and amplitude modulation of an optical guided mode. This regime is in contrast to more conventional optomechanical coupling by way of moving end mirrors in resonant optical cavities. Models are developed and validated for this optomechanical mechanism in a PCW for probe frequencies far from and near to the dielectric band edge (i.e., stop band edge). The large optomechanical coupling strength predicted should make possible measurements with an imprecision below that at the standard quantum limit and well into the backaction-dominated regime. Since our PCW has been designed for near-field atom trapping, this research provides a foundation for evaluating possible deleterious effects of thermal motion on optical atomic traps near the surfaces of PCWs. Longer-term goals are to achieve strong atom-mediated links between individual phonons of vibration and single photons propagating in the guided modes (GMs) of the PCW, thereby enabling optomechanics at the quantum level with atoms, photons, and phonons. The experiments and models reported here provide a basis for assessing such goals.