Kuznetsov claimed the first set 6-2 in 40 minutes before De Minaur pulled the pin, with the 17-year-old citing an abdominal strain after leaving show court one at Sydney Olympic Park.
Thompson lasted 84 minutes in his second-round loss to Kohlschreiber, although the Australian wildcard could see the upside of testing himself in 41C heat.
Thompson doubled the German's five aces but failed to save a single break point, admitting he struggled in the key moments of the match.
The 22-year-old, who is yet to progress beyond the first round of the Australian Open, suggested the stifling heat that struck his home city could actually be beneficial.
"Playing in these conditions, it's good preparation (for the Australian Open)," Thompson said.
"It definitely can't hurt.
"It was pretty warm ... (but) I don't think it was too bad. It was just really tricky conditions. It was a little bit swirly at times, 39 degrees, and the balls were flying."
Thompson, who unravelled after being broken at 5-5 in the opening set, vowed to learn from his final singles match before the Open.
The Sydneysider, who defeated David Ferrer at the Brisbane International last week and also won last week's doubles final with Thanasi Kokkinakis, added belief would not be an issue at Melbourne Park.
"The main thing is just getting matches. I think matches builds confidence," he said.
"I have won plenty of matches already (in 2017). Won doubles matches as well. I'll be pretty confident.
"It's prepared me for the Aussie Open."
Barton, gunning for his maiden ATP quarter-final appearance, fought back in stifling heat to send his match against Muller into a deciding set.
But he was eventually ousted 6-1 3-6 6-4 in just under two hours.