Courses generally provide/source their own - use of town water is limited to a few courses with shortfalls, and only for greens for survival. Horrenduosly expensive in Australia (can be $2 to $3 per kilolitre).
Water is from a mix of on-course dams, water harvesting and bores.Bore levels are closely monitored to prevent excessive draw down.Some clubs take run-off from neighbouring suburbs.Royal Adelaide, Glenelg and Grange in Adelaide all take road surface run-off in winter, pass it through wetlands and pump it into the aquifer. Then retrieve the water in the summer.Royal Adelaide puts in 200 GL a year, and extracts that amount in summer. Salt levels have halved to about 500 parts since the aquifer pumping started.
Royal Melbourne has recently added a couple of water storage facilities following the droughts of a decade ago when ground water salinities rose quickly.
One course is Sydney taps into a major sewer, treats that water on-site and uses that on the course.Treated sewage effluent is used at several courses (Horsham,in the middle of the western desert between Melbourne and Adelaide does this).
It would be rare to see roughs irrigated in Australia, and drought-tolerant grasses are the norm on fairways.
Note that heatwaves are quite different to droughts - Adelaide can easily have several months without rain, Melbourne can be weeks without rain. A dry spring really complicates a dry summer, irrespective of how severe the temperature gets.