This term is applied especially to newspapers. Newsprint used to be printed by a process called 'hot metal printing', which involved molten lead being introduced into a mould to form the printing block. Although the term only really makes literal sense for printed items which use that process, it is by extension now also used figuratively to refer to anything that is fresh and newly made.
Hot off (or from) the press (or presses) didn't originate as a phrase until the 20th century. For example, this from an advertisement in the New Jersey newspaper The Trenton Evening Times, July 1910:
Just hot off the press and a strictly up-to-date cut price sheet of great value to housekeepers.
The hotness is a clear allusion to the hot metal process, but may also allude to an usage of the phrase hot news, i.e. striking or sensational news. This was used in a Daily Express story in September 1914:
'Hot news' ... must be provided for the people, and thus we learn from the Vienna 'Abendblatt' that General French is a prisoner.
