Radwanska has now sealed her place in the quarter-finals of the tournament.
The world number four from Poland saw off the Japanese veteran 6-4 6-3, but admitted it was not easy to finish her match as temperatures at Sydney Olympic Park soared to 44 degrees Celsius.
She said: "Today [Tuesday] was one of the hottest days I've played for sure.
"This is too hot to play tennis, for players, for ball kids, for people sitting out there, I think it's just too hot.
"We just see each other in the locker room after the matches and I think all of us just saying that it's too hot. Sometimes you're playing because it's automatic thing and sometimes not thinking because it's just so hot that you cannot really."
Radwanska, looking to build on her title success in Auckland last week, added: "I was trying to play the same game, the same tennis, but sometimes you're just more fighting against yourself just to stay there than against your opponent.
"I think my fitness is good, I was really working hard in the off-season and I've never had a problem with my fitness.
"But sometimes the sun is too much and it feels like I cannot even finish my match."
There were also second-round victories for Angelique Kerber, Sara Errani and Li Na as the top four women's seeds safely progressed to the last eight.
Second seed Kerber beat Galina Voskoboeva 6-2 7-5, number three Errani was a convincing 6-1 6-1 winner over Maria Kirilenko while Li, the fourth seed who was victorious in Shenzhen last week, was similarly clinical in seeing off Ayumi Morita 6-1 6-0.
It was not such a good day for seventh seed Caroline Wozniacki, though, with the Dane tumbling out 7-6 (7/4) 1-6 6-2 at the hands of two-time grand slam winner Svetlana Kuznetsova.
Watch: Wozniacki falls, Li Na wins in Sydney... More Videos
The other second-round winners were Dominika Cibulkova, Roberta Vinci and 16-year-old American Madison Keys.
In the men's event, Grigor Dimitrov was unable to follow up his impressive showing in Brisbane, where he reached his maiden ATP final before losing to Andy Murray, as he was a first-round casualty, going down 6-3 6-1 to Fabio Fognini.
Sixth seed Radek Stepanek started his tournament on a winning note, beating Guillermo Garcia-Lopez 6-2 6-3, but seventh seed Jeremy Chardy tumbled out at the hands of another Spaniard, losing 6-7 (2/7) 7-5 6-3 to Feliciano Lopez.
Lopez will now play South African Kevin Anderson, who beat Aljaz Bedene 6-3 3-6 6-3, with other first-round victors including defending champion Jarkko Nieminen, Ryan Harrison, John Millman and Bernard Tomic.