  Moons orbiting exoplanets ("exomoons") may hold clues about planet formation,
migration, and habitability. In this work, we investigate the plausibility of
exomoons orbiting the temperate ($T_\text{eq}=294$ K) giant ($R = 9.2$
R$_\oplus$) planet HIP 41378 f, which has been shown to have a low apparent
bulk density of $0.09\,\text{g}\,\text{cm}^{-3}$ and a flat near-infrared
transmission spectrum, hinting that it may possess circumplanetary rings. Given
this planet's long orbital period ($P\approx1.5$ yr), it has been suggested
that it may also host a large exomoon. Here, we analyze the orbital stability
of a hypothetical exomoon with a satellite-to-planet mass ratio of 0.0123
orbiting HIP 41378 f. Combining a new software package, astroQTpy, with REBOUND
and EqTide, we conduct a series of N-body and tidal migration simulations,
demonstrating that satellites up to this size are largely stable against
dynamical escape and collisions. We simulate the expected transit signal from
this hypothetical exomoon and show that current transit observations likely
cannot constrain the presence of exomoons orbiting HIP 41378 f, though future
observations may be capable of detecting exomoons in other systems. Finally, we
model the combined transmission spectrum of HIP 41378 f and a hypothetical moon
with a low-metallicity atmosphere, and show that the total effective spectrum
would be contaminated at the $\sim$10 ppm level. Our work not only demonstrates
the feasibility of exomoons orbiting HIP 41378 f, but also shows that large
exomoons may be a source of uncertainty in future high-precision measurements
of exoplanet systems.
