See Q+A 14
http://www.bom.gov.au/climate/change/acorn-sat/documents/ACORN-SAT_TAF_Short_FAQ.pdf
Although heat island effect isn't anything like the big deal it gets made out to be on these threads, BoM state they additionally take account of it by excluding stations that would be affected by it from their long term trend analysis.
There is some discussion on the (small) impact of UHI effect, and reference to a few papers studying that, here:
https://skepticalscience.com/print.php?r=52
That includes discussion on specific urban heat island effect adjustments made with US data.
For the Melbourne area, Laverton and Melbourne ACORN SAT sites are the two used. Description of their location and environs is here, They fit with the description if the type of sites described in the article above as not displaying significant heating effect and frequently actually showing some cooling influence, albeit overall with no significant impact.
http://www.bom.gov.au/climate/data/acorn-sat/stations/#/86338
http://www.bom.gov.au/climate/data/acorn-sat/stations/#/87031
A map of the overall Aus sites included is here
http://www.bom.gov.au/climate/data/acorn-sat/#tabs=Data-and-networks
