The Noachian climate of Mars is thought by many to have been “warm and wet”, characterized by a global mean annual temperature (MAT) >273 K and abundant rainfall infiltrating into the groundwater system. In this “warm and wet” scenario, when the groundwater system was in contact with the surface in the northern lowlands, a groundwater-fed ocean could form. In contrast, 1-dimensional climate models and 3-dimensional general circulation models (GCMs) are unable to reproduce long-lived, continuous “warm and wet” conditions due to the influence of the faint young Sun when considering a pure CO2-H2O atmosphere; these models instead predict “cold and icy” conditions, characterized by MAT ~225 K and water trapped as snow and ice in the southern highlands. Furthermore, a kilometers-thick globally continuous cryosphere is predicted in this “cold and icy” scenario, precluding direct connection of the groundwater system and the surface, and disfavoring a Noachian northern lowlands ocean. However, global MAT values lack information about regional and seasonal temperature variations, which may vary significantly from global MAT. In this work, we explore whether regional or seasonal temperature variations could permit the formation of a Noachian ocean in a climate with global MAT <273 K. We use a combination of a 3D climate model and a 1D thermal model to determine the climatic conditions in which the required criteria for groundwater release could be met: (1) temperatures above 273 K, required for there to be no cryosphere preventing the groundwater from being released onto the surface, and (2) a sufficiently large groundwater reservoir, required for the groundwater table to intersect the surface. Our results suggest that the formation of a groundwater-fed ocean does not require a continuous and long-lived “warm and wet” climate with global MAT >273 K. If the long-lived Noachian global MAT was >255 K (~30 K above the nominal ambient “cold and icy” climate) and the subsurface contained >63 m global equivalent layer (GEL) of groundwater, then groundwater could be released onto the surface and pond on the floor of the Hellas basin; global MAT >258 K and a subsurface water inventory of >170 m GEL are required for release of groundwater into the topographically lowest regions of Utopia Planitia. If a subsurface water reservoir of ≥770 m GEL existed and local MAT was ≥273 K at Utopia, groundwater release could occur at Utopia and lead to flooding of the northern lowlands and formation of an ocean up to the level of Contact 1. Further, in a “cold and icy” MAT 225 K climate, short-term punctuated heating that raised global MAT to >255 K for at least a few thousand years could lead to groundwater release and flooding of the lowest points on Mars. Under the influence of these very cold climates (global MAT ~255–260 K), these bodies of water would remain ice-free for a geologically short period of time, possibly only a few hundred days, and would completely freeze and sublime in only a few thousand years.