Australia took full control of their second Test against South Africa on day two, racing away to a commanding lead behind David Warner's double century.

After bowling out the South Africans for 189 on Boxing Day, Australia started Tuesday's play at 45-1 and piled on another 341 runs.

They were led by Warner in his 100th Test, as he survived some adversity and went on to post 200 before retiring hurt as his persistent cramps worsened in the blisteringly hot MCG conditions.

He reached his 200 in 254 deliveries, joining Joe Root as the only other player to score a double ton in their 100th Test.

Marnus Labuschagne was run-out for 14 following a mix-up during an overthrow, bringing Steve Smith to the middle, and he made his way to 85 off 161 deliveries before edging to the slips as Australia looked to up the run-rate.

Travis Head continued the high-action style with 48 not out from 48 deliveries, capping a 155-run third session to reach stumps at 386-3, leading by 197 runs.

Anrich Nortje was the visitors' most efficient bowler, with the right-arm quick in taking 1-50 from his 16 overs.

Australia could face some headaches with their bowling stocks in the second innings, with Cameron Green being forced to retire hurt after copping a bouncer on the finger, which immediately swelled up and ended his day on six runs.

Green's status for the second inning is in doubt, while Mitchell Starc's finger injury has already ruled him out of the third Test, implying he will not be able to continue bowling.

Labuschagne gives Warner a lifeline in milestone Test

Warner's day could have looked very different had Labuschagne not opted to fall on his sword.

With Warner on 47, he took an easy single, before calling for a risky second on an overthrow. Labuschagne had run through the crease on the first run, and by taking off for a second, it meant whoever was heading to the bowler's end had no hope.

Luckily for Warner, it was Labuschagne who made the turn and charged back unsuccessfully, departing after only 14 runs.

It was Labuschagne's fifth Test run-out, and since his debut no player has more in the format. Root, Babar Azam and Tim Southee all have four.

Aussies handle the heat

With temperatures in Melbourne hovering around 37 degrees Celsius, it was the Australians who handled the conditions in the draining second session.

In a completely one-sided period of play, the duo of Warner and Smith piled on 97 runs without a wicket from the 27-over session, racing to the lead and building a winning platform.