  Despite decades of scientific research on the subject, the climate of the
first 1.5 Gyr of Mars history has not been fully understood yet. Especially
challenging is the need to reconcile the presence of liquid water for extended
periods of time on the martian surface with the comparatively low insolation
received by the planet, a problem which is known as the Faint Young Sun (FYS)
Paradox. In this paper we use ESTM, a latitudinal energy balance model with
enhanced prescriptions for meridional heat diffusion, and the radiative
transfer code EOS to investigate how seasonal variations of temperature can
give rise to local conditions which are conductive to liquid water runoffs. We
include the effects of the martian dichotomy, a northern ocean with either 150
or 550 m of Global Equivalent Layer (GEL) and simplified CO$_2$ or H$_2$O
clouds. We find that 1.3-to-2.0 bar CO$_2$-dominated atmospheres can produce
seasonal thaws due to inefficient heat redistribution, provided that the
eccentricity and the obliquity of the planet are sufficiently different from
zero. We also studied the impact of different values for the argument of
perihelion. When local favorable conditions exist, they nearly always persist
for $>15\%$ of the martian year. These results are obtained without the need
for additional greenhouse gases (e.g. H$_2$, CH$_4$) or transient
heat-injecting phenomena (e.g. asteroid impacts, volcanic eruptions). Moderate
amounts (0.1 to 1\%) of CH$_4$ significantly widens the parameter space region
in which seasonal thaws are possible.
