We demonstrate a high sensitivity all-fiber spectroscopic methane sensor based on photothermal interferometry. With a 2.4-m-long anti-resonant hollow-core fiber, a 1654 nm distributed feedback laser, and a Raman fiber amplifier, a noise-equivalent concentration of ${\sim}{4.3}\;{\rm ppb}$ methane is achieved at the room temperature and pressure of ${\sim}{1}\;{\rm bar}$. The effects of temperature on the photothermal phase modulation as well as the stability of the interferometer are studied. By introducing a temperature-dependent compensation factor and stabilizing the interferometer at quadrature, signal instability of ${\sim}{2.1}\%$ is demonstrated for temperature variation from 296 to 373 K.