The Russian number 3 seed beat Andrey Rublev 6-4, 6-3, 6-4 at Flushing Meadows in New York but was clearly feeling the effects of the searing temperatures and humidity.
During the final set, he looked into a courtside TV camera and warned that a player is "gonna die" in the nearly 95-degree conditions.
Medvedev, the 2021 US Open champion, will face defending men's champion Carlos Alcaraz next.
Issuing what sounded like a mix between a warning and a plea, Medvedev said: "You cannot imagine. One player (is) gonna die, and they’re gonna see."
Speaking after the match, he added: "The only thing that is a little bit, let’s call it dangerous, is that the question is: How far could we go?
"I’m not sure what can we do.
"Because probably we cannot stop the tournament for four days - because it’s been, what, three, four days it’s been brutal like this?
"It basically ruins everything: the TV, even the tickets, everything. It ruins everything."
Measures have been taken during the tournament to help players deal with the heat including the use of ice as well as courtside tubes blowing cold air to try to stay cool.
Medvedev used an inhaler during a second-set changeover on Wednesday while being looked at by a doctor, who checked his breathing with a stethoscope.
"At the end of the first set, I couldn’t see the ball anymore," he said, adding that he looked across the net at number 8 seed Rublev - his countryman, friend, and godfather to his daughter - and thought: "Wow. It seems like he cannot run anymore."
Medvedev said he felt dizzy afterward and that both he and Rublev rubbed their faces raw by toweling off so frequently.
Rublev described feeling his heart racing between points, but asked about his level of concern on a day like that, he said: "I’m not even thinking about my health."
Under a new rule adopted on Tuesday for the rest of the event, the US Tennis Association partially closed the retractable roof on the Arthus Ashe court - normally used to block out rain - to provide some additional protection from the sun for spectators and competitors.
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