The daily maximum and minimum temperatures in Melbourne, Australia, for the period 1981–1990 are examined in this article by means of fractional integration techniques. Using a parametric testing procedure (Robinson 1994), the results show that the time series for both datasets can be specified in terms of fractionally integrated statistical models: the maximum temperatures with orders of integration slightly smaller than 0.5 and the minimum temperatures with values slightly higher. Thus, the temperatures seem to be stationary in the case of the maximum values and non-stationary for the minimum ones, but mean reverting in both cases. Moreover, no significant trends in the model were found, implying that there is no evidence of climatic change in the data, at least for the period 1981–1990.