Freezing from the Cradle Mountain cold, Malcolm Turnbull hugged the Tasmanian premier.
As Will Hodgman pledged to keep fighting for his state's share of the GST, the prime minister's arm came around him.
"I'm just warming him," Mr Turnbull told reporters at the icy mountain lake.
"This is a political hug ... designed to provide thermal comfort."
A very cold Mr Hodgman was asked about fighting for Tasmania's revenue share of the GST, but he had other immediate issues to deal with.
"The biggest problem I've got is my mouth's not working because it's cold," the premier said.
"I feel like I've had an anaesthetic or something. You can take a tooth out and I wouldn't feel it."
Mr Turnbull promised Tasmania won't lose a cent out of any changes to the way the tax revenue is carved up.
"The dollars it receives are not going to go backwards," he said.
But the prime minister acknowledged states need more certainty for planning, with payments fluctuating too much each year.
He wouldn't confirm when a Productivity Commission review into possible changes will be publicly released - or if it will come before upcoming by-elections in Tasmania, South Australia, WA and Queensland.
"It will be released within weeks not months, but it's a huge report ... I haven't had the opportunity to read it, it's over 400 pages I might add, it's quite a doorstopper," Mr Turnbull said.
Treasurer Scott Morrison has the report and is going through it, but shadow treasurer Chris Bowen says it must be released before the by-elections.
"It doesn't need weeks. It should be released this week," Mr Bowen told the National Press Club.
The commission's interim report said the system - known as horizontal fiscal equalisation - should use the second-strongest state or average as the basis of the carve-up, rather than the strongest.
State and territory treasurers plan to meet in Melbourne next week to discuss their priorities for reform.
The coalition is aiming to win by-elections in Tasmania and South Australia, both of which rely on extra GST revenue from the other states.