Mitchell Dale Stehling told his wife and parents he was going to hike to the Spruce Tree House, which is a cliff dwelling on the Chapin Mesa in the park.
When Stehling did not return Sunday, family alerted park officials.
Park crew members searched Spruce Canyon, Spruce Tree House, Petroglyph Trail and other trails on Chapin Mesa.
Crews resumed their search early Monday, expanding the search area, searching by foot, horseback and helicopter. Two dog teams from Dolores Canine Search and Rescue also were assisting.
About 30 people were involved Monday as temperatures reached 102 degrees in the canyons.
Rescue workers continued to search Tuesday with 60 to 70 searchers, including 20 members from the San Juan National Forest Hot Shots.
Temperatures in the park were in the 90s. The terrain consists of steep canyons and mesa tops at elevations between 6,500 feet and 8,000 feet.
Stehling was last seen wearing a brown shirt and hat, khaki shorts and hiking boots. He was not carrying any water or other gear.