If you really want to terraform a world like Ganymede, you will need to go very big indeed. LDutch's answer provides the context, but where are we going to get the energy to heat the moon, especially when you are so far from the Sun?
I'm going to suggest a laser, but not just some piddly little gigawatt thing orbiting Mercury, but actively engaging the Solar photosphere in order to use it as a lasing medium. (Note, there was an article called "Constructing artificial laser stars" by John Talbot, but this seems to have vanished from the Internet). Simply put, the plasma environment of the photosphere makes for a powerful lasing medium, so a "starter" laser to create a population inversion can trigger a massive, terawatt laser pulse. Ringing the Sun with mirrors to create a circular "racetrack" for the laser pulse gives the medium far more material to lase, and at the appropriate time, one of the mirrors can be manipulated to allow the beam to exit.
From the article:
- Orbiting Mirrors
The mirror method would extract laser energy by creating a resonant cavity in which the radiation would make multiple passes dramatically increasing the effective gain. The path would ideally be perpendicular to any velocity gradient in order to reduce Doppler smearing and increase coherence and thus directivity. The laser beam is emitted tangential to the surface of the star.
Sherwood (1988) described a platoon of orbital mirrors around mars or venus to extract a coherent and directed CO2 laser beam from the gain medium. He foresees the use as means of transmitting/propagating our entire culture to a future nano-civilisation established in various other solar systems throughout our galactic neighborhood.
Mirrors external to the stellar atmosphere would reduce the problems of erosion and orbital deflection by the violent and corrosive stellar winds. Although pairs of mirrors would be ideal to extract directed energy from the gain medium, there are power limitations due to the finite reflectivity of the mirrors (which absorb a small but damaging fraction of the radiation). To overcome this problem larger mirrors could be constructed to distribute the heat load, and reduce the Airy diffraction pattern (beam divergence). However large mirrors are extremely vulnerable to orbital debris such as an encounter with a handful of sand from an intersecting orbit etc...
Large mirrors will act like solar sails, this side-effect could be used to maintain a stationary satellite (statite) over the desired location near the solar limb. (see papers on 'statites' by R.L. Forward) The photon pressure from the laser photons and the photosphere could be adjusted to exactly compensate for the solar gravitational force and prevent the hovering statite from falling onto the star's surface. Conservation of momentum would impart a momentum of 2p every time a photon bounced off the mirror. For a multiple pass optical cavity the photon travels back and forth many times stimulating emissions at every pass. The force on the mirrors from this photon pressure in combination from the photon pressure from the star's photosphere acts like a solar sail and can be designed to exactly balance the inward gravitational force pulling the mirror onto the star. These three counterbalancing forces could be harnessed to maintain the mirror stationary against the gravitational pull of the star. ('statites' or stationary satellites by R.L.Forward). Very near the star there may be deviation from 1 over r squared law by dilution of radiation effect of finite angular width of solar disk.
If more than two mirrors are used a ring laser could be produced, the radiation would make numerous quasi-circular trips around the sun; in other words, a photon merry-go-round spinning at the speed of light !
The other thing you will need is a series of mirrors out of the plane of the ecliptic in order to steer the beam, since the motion of Jupiter as it orbits the Sun and the orbit of Ganymede will mean the beam needs to be actively controlled at all times.
This principle can be extended throughout the Solar system, and the beam used as a high quality energy source deep into the Oort cloud if desired.
As for the target, the intense energy from the beam will be defocused somewhat by the targeting mirror(s), likely hovering above the Jovian pole, and steered much like solar sails using the laser energy. Since the builders have so much energy at their disposal, they can indulge in all kinds of exotic engineering projects, but the most likely one would be to simply create a huge "balloon" for Ganymede to be enclosed in. This would help diffuse the laser light, trap the heat and atmosphere and provide some fine control for the project managers on the surface (for example, if the laser is turned off for a short time for maintenance, or to realign the beam with another mirror, the heat energy and gasses remain trapped inside the balloon structure).
Frankly, if you are going to terraform or use super science, then you really need to go "big" with your plans.