  Free-floating planets (FFPs) can result from dynamical scattering processes
happening in the first few million years of a planetary system's life. Several
models predict the possibility, for these isolated planetary-mass objects, to
retain exomoons after their ejection. The tidal heating mechanism and the
presence of an atmosphere with a relatively high optical thickness may support
the formation and maintenance of oceans of liquid water on the surface of these
satellites. In order to study the timescales over which liquid water can be
maintained, we perform dynamical simulations of the ejection process and infer
the resulting statistics of the population of surviving exomoons around
free-floating planets. The subsequent tidal evolution of the moons' orbital
parameters is a pivotal step to determine when the orbits will circularize,
with a consequential decay of the tidal heating. We find that close-in ($a
\lesssim 25 $R$_{\rm J}$) Earth-mass moons with CO$_2$-dominated atmospheres
could retain liquid water on their surfaces for long timescales, depending on
the mass of the atmospheric envelope and the surface pressure assumed. Massive
atmospheres are needed to trap the heat produced by tidal friction that makes
these moons habitable. For Earth-like pressure conditions ($p_0$ = 1 bar),
satellites could sustain liquid water on their surfaces up to 52 Myr. For
higher surface pressures (10 and 100 bar), moons could be habitable up to 276
Myr and 1.6 Gyr, respectively. Close-in satellites experience habitable
conditions for long timescales, and during the ejection of the FFP remain bound
with the escaping planet, being less affected by the close encounter.
