The Scot, who beat Novak Djokovic in five sets to clinch his first Grand Slam title in the USA last year, booked his place in the fourth round at Flushing Meadows with a 7-6 6-2 6-2 win over Florian Mayer.
Once again the 26-year-old said that the hot and humid weather was difficult to come to terms with on Arthur Ashe, but remains hopeful that conditions will improve as the tournament progresses.
"At the end of the first set and for the second set it was extremely hot," Murray said in his on-court interview.
"We have been told the sun is coming so hopefully that will take away some of the humidity over the next few days.
"There might be more pressure for me to win from the outside, but I feel a lot more comfortable coming into these events than I did this time last year."