On a day which brought temperatures in the low 40s in the shade and 10 degrees hotter on the field, the Australians were 357 for four at tea on Saturday, with Michael Clarke not out on 73.
Mike Hussey and Clarke added 151 for the fourth wicket until Hussey fell in the final over before tea.
The overall lead at tea was 386 with the home side looking to set the tourists a massive fourth innings run chase. The Australians, already 2-0 up in the series, would regain the Ashes with victory here.
It was proving a horror day for the English, who showed great spirit but could only watch the Ashes slipping away as they not only bowled without luck, but had to contend with energy-sapping heat in the field.
A number of catches went begging, Geraint Jones missed a stumping and confident appeals were turned down as just three wickets fell in the first two sessions.
Hussey, controversially overlooked during the entire 2005 Ashes series in England, continued his incredible run at the top level when he notched his maiden Test century against England and his fifth overall.
The left-hander pulled the unlucky Steve Harmison straight down the ground for his 12th four to bring up the milestone in 213 minutes from 148 balls.
Averaging 86.33 in Test cricket with the bat, Hussey eventually fell for 103, caught behind to give spinner Monty Panesar (2-92) his second victim for the day and seventh for the match.
Hussey had enjoyed his share of good fortune, given not out on 15 to an appeal for a catch at bat-pad from Panesar's bowling when replays showed he appeared to get bat on ball. Hussey also had lives on 48 and 78 when he was missed by Jones and Andrew Strauss respectively.
Earlier, opener Matthew Hayden missed out on a century when he fell for 92, while Australian captain Ricky Ponting made 75.
Ponting was in an aggressive mood and looked set for another big score as he passed the 500-run mark for the series, but he pushed hard at a Harmison delivery and got an outside edge to Jones.
Hayden lived dangerously and his extravagant shot selection came back to haunt him when he tried to cut against the spin of Panesar and was brilliantly caught at the second grab by Paul Collingwood at first slip.
Highlighting the enormity of the task facing England, the highest successful fourth innings run chase at the WACA is 342, when Australia beat India back in 1977.
Australia 244 and 357 for 4 ( Hussey 103, Ponting 75, Clarke 73 n o; Panesar 2 for 92, Hoggard 1 for 60) Vs England 215