The Stags have an option of signing a permanent deal with the 22-year-old striker.
Coulthirst, a graduate of Tottenham's academy, made just one first-team appearance while at White Hart Lane.
The striker also had loan spells with Leyton Orient, Torquay, Southend, York and Wigan.
Coulthirst will join his former team-mate Hayden White at Field Mill, after he was signed on loan from Posh a week ago.
Find all the latest football transfers on our dedicated page or visit our Premier League tracker here.

Jannette Black, head of Springhill and Auchenback Primary School in Barrhead, East Renfrewshire, was seen at a minor injuries unit on Wednesday.
East Renfrewshire Council confirmed that the incident had taken place and said an investigation into the circumstances was ongoing.
Police Scotland said the incident had not been reported to them.
A council spokesman said: "We can confirm that an incident took place at the school [on Wednesday].
"No serious injuries were sustained and the member of staff involved did not require hospital treatment, however, did attend a local minor injuries unit as a precaution.
"Incidents of this nature are extremely rare in our schools and we have a zero tolerance approach to violence at work."
The local authority rejected claims that the incident was the latest one linking the school with anti-social behaviour or a lack of action by the council's education department.
A statement said: "Any incident relating to violence which is reported to us is investigated thoroughly and the appropriate action taken.
"We do not accept the claims that have been made about the management of either our schools or the education department.
"In fact, a recent Education Scotland report on this school highlights a number of areas of improvement which have been achieved under the current management."
League Two side Mansfield Town have signed Peterborough United forward Shaquile Coulthirst on loan until the end of the season.
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A primary school head teacher was taken to hospital following an attack by a pupil.