Solid-state light detection and ranging, capable of performing beam scanning without using any mechanical moving parts, requires a phase-modulator array. Polymers facilitate the fabrication of efficient phase modulators with low drive power, owing to their high thermo-optic (TO) effect and low thermal conductivity. We designed and fabricated a polymeric phase-modulator array and analyzed the temporal response of the TO phase modulator. The frequency response of the phase modulator was measured for a Mach-Zehnder interferometer (MZI), and the transfer function was modeled in terms of multiple poles and zeros. The frequency response of a fabricated beam-scanning device incorporating the TO phase modulator was also measured. The temporal response of the beam scanner was confirmed to coincide well with that of the MZI modulator. The device exhibited a fast rise time of 12 ms, accompanied by slight power variations appearing for a long period (over hundreds of seconds), which originated from the inherent viscoelastic effect of the polymer materials.