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.
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League Two side Mansfield Town have signed Peterborough United forward Shaquile Coulthirst on loan until the end of the season.