Recent studies have shown that large exomoons can form in the accretion disks around super-Jovian extrasolar planets. These planets are abundant at about 1 AU from Sunlike stars, which makes their putative moons interesting for studies of habitability. Technological advances could soon make an exomoon discovery with Kepler or the upcoming CHEOPS and PLATO space missions possible. Exomoon climates might be substantially different from exoplanet climates because the day-night cycles on moons are determined by the moon's synchronous rotation with its host planet. Moreover, planetary illumination at the top of the moon's atmosphere and tidal heating at the moon's surface can be substantial, which can affect the redistribution of energy on exomoons. Using an idealized general circulation model with simplified hydrologic, radiative, and convective processes, we calculate surface temperature, wind speed, mean meridional circulation, and energy transport on a 2.5 Mars-mass moon orbiting a 10-Jupiter-mass at 1 AU from a Sun-like star. The strong thermal irradiation from a young giant planet causes the satellite's polar regions to warm, which remains consistent with the dynamically-driven polar amplification seen in Earth models that lack ice-albedo feedback. Thermal irradiation from young, luminous giant planets onto water-rich exomoons can be strong enough to induce water loss on a planet, which could lead to a runaway greenhouse. Moons that are in synchronous rotation with their host planet and do not experience a runaway greenhouse could experience substantial polar melting induced by the polar amplification of planetary illumination and geothermal heating from tidal effects.