David McIlveen, who is still a member of the party, said Mrs Foster had "seriously misjudged" public anger.
Mrs Foster set up the RHI scheme in 2012, but its lack of cost controls has left NI taxpayers with a Â£490m bill.
A DUP spokesperson said she continued to receive "overwhelming support" within the party and beyond.
"Former MLA David McIlveen is entitled to his personal opinions, however, this is the first time that he has articulated any view since losing his seat," they said.
On Wednesday, the party said the assembly may be recalled next week to approve emergency legislation to deal with the overspend.
Mr McIlveen, who is the son of Free Presbyterian minister and close friend of the late Rev Ian Paisley, Rev David McIlveen, questioned Mrs Foster's handling of RHI in an article for the News Letter.
He suggested Mrs Foster was personally responsible for turning the scheme into an "omnishambles" and said she will come under increased pressure from her own party.
He drew comparisons with the treatment of former DUP leaders Peter Robinson and the Rev Ian Paisley.
Mr McIlveen wrote that Mrs Foster was now "deeply damaged" and unlikely to lead the party into the next election after becoming an "electoral liability".
"Does a party obsessed with elections want to move forward with a leader who appears incapable of facing up to their mistakes?" he asked.
"The RHI scandal was most likely driven more by a desire to curry favour with the rural electorate than anything more sinister.
"Whilst the view in public is that Arlene's team are as loyal and happy as ever, the reality in private is something very different."
The party's East Antrim MP Sammy Wilson dismissed Mr McIlveen's comments.
He asked what was more credible: "The views of one individual who will have his own motivations, or the views of the vast majority of party members who have publicly come out and given their support to Arlene Foster.
"I think that I am maybe in a better position than David McIlveen to make an assessment of the view within the party."
However, Ulster Unionist leader Mike Nesbitt said Mr McIlveen's intervention was "significant".
"I know you were reporting it as David McIlveen breaking ranks and that is true, but equally true is that he is joining the ranks of those pointing the finger of blame," he said.
"And we're not talking about bit players here, David McIlveen was an assembly private secretary for Arlene Foster, he's joining Jonathan Bell who was a junior minister and also a minister for the department of enterprise."
Mr McIlveen also criticised Mrs Foster's treatment of Jonathan Bell, who in December, made a series of allegations about the DUP's involvement in the scheme.
"When one of her own party members broke rank to express their concern about the scheme, rather than approach the issues raised with a listening ear, the default position was to attack the personal integrity of the individual raising the concerns," he wrote.
"In any other context, Jonathan Bell MLA would be called a whistleblower.
"Upon witnessing the way in which he was treated by the leadership of the party I do not see how any member of the public who sees something going wrong in the civil service would feel inspired to raise issues with a DUP-run department, upon witnessing how their own people are treated."
Last month, Mrs Foster said she had  "felt intimidated by Jonathan Bell" during an RHI meeting, claiming he had "used his physical bulk to stand over me in quite an aggressive way".
Mr Bell had claimed that Mrs Foster was verbally "abusive" and angrily "overruled" him when he tried to close the scheme.
Mr McIlveen also criticised Mrs Foster for branding some of her RHI  critics as "misogynist", saying that "rather than facing critics on the level of their political arguments yet again it descends to the personal".
Mr McIlveen, who lost his seat in last May's election, claimed the DUP was "obsessed with elections".
A former DUP MLA has broken ranks and criticised the party leader Arlene Foster, saying the Renewable Heat Incentive scheme is an "omnishambles".