With the mercury nudging 40 degrees at Homebush, the world No. 22 and second seed Cuevas got one back on the Frenchman after losing their first meeting in Rome last year.
Cuevas will face the sixth-seeded Gilles Muller, after the 33-year-old knocked Australian qualifier Matt Barton out of competition.
The Australian contingent struggled through the stifling heat with Barton falling short of his maiden ATP quarter-final appearance at the Sydney International, while compatriot Jordan Thompson was also eliminated.
Barton lost a sapping three-setter to Gilles Muller on Wednesday, when Thompson went down 7-5 6-4 to Philipp Kohlschreiber as the temperature soared.
Barton fought back from one set down in the stifling heat to send his match into a deciding set, but was eventually ousted 6-1, 3-6, 6-4 in just under two hours.
Kohlschreiber needed just 84 minutes to cruise past Thompson, who doubled the German's five aces but failed to save a single break point.
Thiem plays his first match of the Australian Open warm-up event in the feature night match, taking on Portuguese qualifier Gastao Elias.