The vote followed nearly an hour of debate by the board.
Coleman's supporters pointed to his experience managing the schools for the deaf and the blind and as a former state school board member.
"I have been absolutely deeply, deeply impressed by Superintendent Coleman and the team he has surrounded himself with," said board member Jennifer Johnson.
Board member Heather Groom also pointed out that though she is concerned about the lawsuit filed by Coleman's wife, it hasn't been a conflict in his work as a superintendent so far.
Other board members, however, said they simply couldn't get past it
Coleman's wife Kim Coleman alleges in the lawsuit that the State Charter School Board violated law in ousting her in 2009 as director of West Valley City's Monticello Academy.
The lawsuit names as defendants state director of charter schools Marlies Burns and members of the state charter school board, among others.
The case is now in U.S. District Court.
"What I think is absolutely clear is that Joel Coleman is involved in this," said board member Kim Burningham. "I think for us to put in as an interim superintendent a person with such a difficult conflict will discourage people in the state office, it will hurt morale further."
Board member Terryl Warner, who wrote an email Sunday night to other board members asking for the public vote, questioned the logic of appointing someone who has an active lawsuit against the agency he'd be heading.
"I just don't understand how we're looking at appointing somebody who's involved, actively involved [in the lawsuit]," Warner said.
Board member Dave Thomas, however, said Joel Coleman will not be over Burns nor interact with the charter school board because of the lawsuit. Rather, the interim deputy superintendent Sydnee Dickson, state office director of teaching and learning, also appointed Thursday night will handle those functions.
Attempts to reach Joel Coleman for comment after Thursday night's vote were not immediately successful.
Some also criticized Joel Coleman's lack of public school teaching experience. Coleman has spent his career as a seminary teacher and administrator for The Church of Jesus Christ of Latter-day Saints.
Board member Debra Roberts said the local district superintendents with whom she's met said they appreciate Joel Coleman as an individual but worried about that lack of experience.
"It was expressed that in those meetings, it became very clear, even with the great job he's doing at [schools for the deaf and blind] he really has very little to no understanding of the way local districts work," Roberts said.
Thomas, however, said, "He's a career professional educator, while not in the public sector, there are many good teachers in the private sector."
The board could appoint a new permanent superintendent as early as the end of September.
Thomas said Coleman will not apply for that permanent position.
The meeting Thursday follows weeks of drama among state education leaders. Earlier this month, deputy superintendent Brenda Hales stopped working, saying she would use her vacation and other leave until her retirement becomes official at the end of the year. Shortly after that, Superintendent Menlove, who had previously announced his retirement, decided he would leave in coming weeks rather than wait for a permanent replacement. Hales has said no particular event spurred her decision.
In her email earlier this week, Warner also asked for an independent investigation into possible misuse of power and authority by fellow board members.
She's declined to detail the specifics. She's also alleging the board discussed topics in closed session that should have been public.