But Svitolina cranked up the heat as temperatures rose on Rod Laver Arena, relentlessly overpowering her opponent from the back of the court to take the final two sets in dominant fashion.
"I thought I was going to melt today, was struggling a bit" Svitolina admitted. "Today I had enough sun, I just want to have an ice bath and recover."
Svitolina came into the first Grand Slam of the year in top form after winning the Brisbane International warm-up event after picking up five WTA Tour titles last year, more than any other woman.
She now faces 15-year-old Kostyuk whose fairytale continued Wednesday as she became the youngest player to reach the third round since Martina Hingis in 1996 in beating local wildcard Olivia Rogowska in straight sets.
Luksika Kumkhum d Belinda Bencic, 6-1, 6-3
Venus Williams' Australian Open conqueror Belinda Bencic ran out of steam Wednesday, failing to keep the momentum going against qualifier Luksika Kumkhum.
The Roger Federer-inspired Swiss stunned Williams in round one, but was no match for the Thai star who moved into a Grand Slam third round for the first time.