The Serb - seeking a fifth-straight final appearance at Flushing Meadows - continued his charge for the trophy with a comfortable 6-1 7-5 6-4 victory over the 22nd seed on Monday.
Djokovic was on court for just over two hours as he set up a meeting with Andy Murray in the quarter-finals, but on a day when temperatures soared into the 80s he conceded he had been asked plenty of questions physically.
"I know that I definitely didn't want to stay too long out there," Djokovic said.
Conditions aside, the world number one was never really in trouble against a spirited Kohlschreiber.
The German did briefly rally in the second, forcing Djokovic to serve to stay in the set, but that was as close as he came to an upset.
Such form from the 2011 champion provided an ominous warning for Murray, who made harder work of beating Jo-Wilfried Tsonga 7-5 7-5 6-4 on Arthur Ashe court to book his own place in the last eight.
Yet Djokovic is taking nothing for granted ahead of their meeting on Wednesday - a repeat of the epic 2012 final.
"You know, as we come closer and closer to the finish line, the matches will get tougher," he added.
"That's where I will see where my game is and if I’m mentally strong enough to hold on."
