We present temperature dependent scanning tunneling spectroscopy data of the quasi-one-dimensional conductor Li0.9Mo6O17. The differential tunneling current in our low-temperature spectra shows a power-law behavior around the Fermi energy, which is expected for a clean Luttinger liquid. The power-law exponent is found to be 0.6. Spectra for a temperature range of 5 to 55 K can be fitted fairly well with a model for tunneling into a Luttinger liquid at the appropriate temperature. A fit with a model based on a zero bias anomaly is significantly worse compared to the Luttinger liquid model. No signature of a phase transition at T = 24 K is observed in our temperature dependent data.