The pair will face questions from an audience of Labour members, Labour voters and former Labour voters on BBC2’s Scotland 2015 programme, presented by Sarah Smith, at 10.30pm.
In May’s election, Labour saw its band of Scottish MPs at Westminster slashed from 41 to just one, with Ian Murray in Edinburgh South the sole survivor.
Polls suggest the party faces another major defeat in the Scottish Parliament elections in May next year.
The contest to replace former leader Jim Murphy, who stepped down after the general election, is a straight fight between Ms Dugdale, a Lothian MSP and former deputy leader, and Mr Macintosh, MSP for Eastwood since the parliament was set up in 1999.
Ms Dugdale is the favourite to win. She has the backing of 30 out of 37 parliamentarians, 80 per cent of Labour councillors, 90 per cent of local parties and the majority of trade unions who have made a nomination.
She said: “I’m standing to not just to lead the Scottish Labour Party but to win back the trust of the people of Scotland.
“This televised debate is a chance to reach beyond our party membership and speak directly to the people who have felt the letdown and who will shape our party’s future – everyday Scots. I’m looking forward to listening to their concerns and making Scottish Labour relevant to their lives again.”
Mr Macintosh last week launched a “members’ tour” to take his message directly to party members in every part of Scotland.
He claimed that undecided Scottish Labour members were responding well to his “detailed plan of change” and moving towards voting for him as leader.
He said: “I think people are crying out for Labour to be more positive and to talk about Scotland’s future. Not only do I intend to be more forward looking, I want to win new members and new supporters to our cause and not just rely on those who have traditionally voted Labour.”
The ballot opened last Monday and will close on Friday, August 14, with the result announced the next day.
The result of the UK leadership contest will not be known until September 12.