Heatwaves represent a significant natural hazard in Australia, arguably more hazardous to human life than bushfires, tropical cyclones and floods. In the 2008/2009 summer, for example, many more lives were lost to heatwaves than to that summer's bushfires which were among the worst in the history of the Australian nation. For many years, these other forms of natural disaster have received much greater public attention than heatwaves, although there are some signs of change. We propose a new index, called the excess heat factor (EHF) for use in Australian heatwave monitoring and forecasting. The index is based on a three-day-averaged daily mean temperature (DMT), and is intended to capture heatwave intensity as it applies to human health outcomes, although its usefulness is likely to be much broader and with potential for international applicability. The index is described and placed in a climatological context in order to derive heatwave severity. Heatwave severity, as characterised by the climatological distribution of heatwave intensity, has been used to normalise the climatological variation in heatwave intensity range across Australia. This methodology was used to introduce a pilot national heatwave forecasting service for Australia during the 2013/2014 summer. Some results on the performance of the service are presented.