Scanning tunnelling spectroscopy (STS) was used to study the Luttinger liquid behaviour of the purple bronze Li(0.9)Mo(6)O(17) in the temperature range 5 K < T < 300 K. In the entire temperature range the suppression of the density of states at the Fermi energy can be fitted very well by a model describing the tunnelling into a Luttinger liquid at ambient temperature. The power-law exponent extracted from these fits reveals a significant increase above 200 K. It changes from α = 0.6 at low temperature to α = 1.0 at room temperature.