With the temperature touching 40C, 17-time grand slam champion Williams brushed aside the challenge of world number 104 Vesna Dolonc with minimal fuss.
Russian-born Serbian Dolonc did excite the crowd on occasion, but those moments were too infrequent and Williams wasted little time in sealing a 6-1 6-2 win in 63 minutes.
She quickly took a 3-0 lead in the opening set after clinically breaking Dolonc in the second game when the 24-year-old hit a backhand long.
It was clear that Williams had no intention of hanging around in the searing heat as she continued to attack her opponent's serve, but a rash of errors saw the American squander two more break points and allowed Dolonc to get on the scoreboard.
That was as good as it got for the underdog, though, who gave up another break of serve before Williams, despite struggling while serving into the sun, wrapped up the first set at the second attempt after just under half an hour.
Dolonc, who beat Spaniard Lara Arruabarrena in the first round, was immediately broken at the start of the second set and conceded another break of serve in the fifth game after three consecutive double faults.
Williams almost surrendered her serve but saved the only break point she faced with an ace before going on to seal victory and set up a clash with either 31st seed Daniela Hantuchova or Karolina Pliskova.