Texas broke into the Top 25 after a pair of solid performances at Madison Square Garden last week.
Playing their next three games in Austin, the 20th-ranked Longhorns have a good chance at moving up the poll.
Texas looks to win its 20th consecutive home game against an unranked opponent when it meets Sam Houston State on Tuesday night.
After a pair of victories at home earlier this month, Texas (3-1) faced its first challenge of the season in the 2K Sports Classic in New York. The Longhorns defeated then-No. 13 Illinois 90-84 in overtime on Thursday before losing 68-66 to No. 5 Pittsburgh on Friday.
"This team has a chance to be pretty good," coach Rick Barnes said. "I think we can play better, but we'll learn from it."
The Longhorns, who are trying to replace three starters from last year, were especially pleased with the effort from their underclassmen. Sophomore Jordan Hamilton scored 53 points and added 15 rebounds over the two games to be named Big 12 player of the week Monday, while freshman Tristan Thompson had 31 points and 13 rebounds during the tournament.
"It's got us ready," Thompson said of facing tough competition, "and it helps us get stronger as a team."
Texas returns home to face a much lighter schedule. After Sam Houston State, the Longhorns will take on Rice and Lamar before going back on the road to meet Southern California on Dec. 5.
Texas hasn't lost at home to an unranked team since falling 69-65 to Missouri on Feb. 4, 2009.
The Longhorns will open the homestand against the defending Southland Conference champions, who are playing their first Division I opponent after victories over Division III's Mary Hardin-Baylor and Northwestern Oklahoma State of the NAIA.
The Bearkats shot 53.0 percent in a 90-68 victory over Northwestern Oklahoma State last Monday, going on a 17-2 run to put the game away late in the second half. Gilberto Clavell had 20 points and 10 rebounds to lead six Sam Houston State players in double-figure scoring.
"Defensively we have to still get better, hold each other accountable and get better every game," forward Josten Crow, who had 11 points, eight assists and seven rebounds, told the team's official website.
Crow is averaging 16.0 points and 10.0 rebounds, while Clavell leads the team with 17.5 points per game.
The two seniors pace a team that lost to Baylor in the opening round of last season's NCAA tournament.
Sam Houston State was especially dangerous from 3-point range last season, ranking ninth in Division I while making 8.7 shots from beyond the arc per game. The Bearkats, though, have made 14 of their 51 attempts (27.5 percent) this season.
The Longhorns defeated the Bearkats 122-71 in 2003 to improve to 11-2 in the all-time series.
