The oxidation kinetics of aluminium films have been studied in the temperature range 330-400 K at a pressure of 0.66 Pa. A special type of quartz crystal microbalance has been developed in order to extend the temperature range of experiments up to 500 K. The vibrating quartz crystal was heated by IR light and the quartz temperature was measured by a thermocouple fixed to the quartz itself. The drift of the quartz frequency could be stabilized to values below 0.5 Hz within 1 h which is equivalent to about 0.1 monolayer (ML) of O-2. The oxidation process on clean film surfaces starts with a very fast initial oxygen absorption step which is completed in less than 1 min. The thickness of the oxide layer after this first stage corresponds to 2-4 ML of oxygen. At temperatures below 350 K further oxidation becomes very slow. At higher temperatures a remarkable enhancement of the oxidation rate occurs and the time law becomes logarithmic. After long exposure times oxide layers with a thickness up to 16 ML are observed. The oxidation curves are compared with results of model calculations based on the Cabrera-Mott theory.