Winker said he couldn't discuss what Becker's motive for the slaying might have been, or what Becker might have been up to in the days leading up to the shooting.
"Motive is one of those things we're looking into," Winker said.
School was not in session, and Becker did not threaten any of the students in the room, he said.
Thomas, 58, died at a Waterloo hospital. His shooting stunned the rural community of 1,800 residents 80 miles northeast of Des Moines, and it reverberated through NFL circles, where he was remembered as much for his faith as his winning record.
"Coach Thomas was very special to me and many other young men from the Aplington-Parkersburg communities," said Green Bay Packers linebacker Aaron Kampman. "His legacy for many will be associated with his tremendous success as a football coach. However, I believe his greatest legacy comes not in how many football games he won or lost but in the fact that he was a committed follower of Jesus Christ."
Named the NFL's 2005 high school coach of the year, Thomas amassed a 292-84 record in 37 seasons as a head coach - 34 of them at Aplington-Parkersburg. He coached several players who went on to the NFL, including Kampman, Jacksonville Jaguars center Brad Meester, Detroit Lions defensive end Jared DeVries, and Denver Broncos center Casey Wiegmann.
Meester said he revered him almost as a father figure, and that his high school coach was able to get the most out of each of his players.
"He's one of those guys that truly cared about every player that was in that program," Meester said in a statement.
"It's just the stuff that he taught every one of us, stuff that I'll never forget. The value of hard work, pride in what you do and just caring about the guy beside you and that's what he did. He cared for each and every one of us that went through that program," he said.
Taylor Schrage, who played for Thomas before moving on to Iowa State, where he suffered a career-ending knee injury, said Thomas cared about him as much after his injury as before.
"It was more than just football. It was how he could try to impact each and every player that he had in a good way, whether it was about faith, hard work, commitment, teamwork," he said.
Schrage said he grew up with Becker, but he declined to comment about him further.
Becker, 24, is charged with first-degree murder and was being held in Butler County jail. The sheriff's office said Becker did not have an attorney, and he was not scheduled for arraignment Wednesday.
Phone messages seeking comment from family members of Becker and Thomas were not immediately returned.
According to court records, Becker threatened a Cedar Falls homeowner with a baseball bat Saturday night, smashed windows at the home and rammed his car through its garage door before leading police on a high-speed chase.
Cedar Falls Police Chief Jeff Olson said Wednesday that Butler County deputies arrested Becker after a chase through Grundy and Butler counties. Deputies agreed to take him to a hospital psychiatric ward and request that Cedar Falls police be notified when he could be released. Cedar Falls police didn't hear anything more, but on Tuesday, Becker was released from custody.
"I don't know what happened," Olson said. "I don't know what we didn't hear back."
It wasn't immediately clear if Becker was taken to the ward. The Sheriff's Office declined to comment on the matter.
Phone messages left with the homeowner, Dwight Rogers, were not immediately returned.
Gov. Chet Culver, who was once a high school teacher and coach in Des Moines, said he was stunned by the shooting.
"As a former high school football coach, I've always had great admiration and respect for Coach Thomas," Culver said in a statement. "The state and national coaching fraternity has suffered a devastating loss. As we mourn the passing of Coach Thomas, it is my hope we can all continue to learn from his example."
Paul Rhoads, Iowa State's new football coach, said in a statement that Thomas was one of the first people to call him when he accepted the Cyclones job last December. Rhoads said Thomas was an Iowa coaching legend and "the best of people."
"His leadership set an example for us and his legacy will live on in the thousands of people he has touched in and out of the classroom and on and off the field," Rhoads said.
Toby Lorenzen, head coach at Central Lyon High School in Rock Rapids in northwest Iowa, said the killing was a blow to Iowa's high school football coaching fraternity.
"He was one of the most down to earth, well respected coaches around."
DeVries, a defensive end with the Lions, walked off the practice field in Allen Park, Mich., toward the end of the team's morning practice. He looked shaken after being informed Thomas died.
Team officials said DeVries was not immediately available for comment.
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