If the gas giant has at least one moon that is suitable for terraforming, an artificial sun can be built which supplies the energy needs. This will work only if the moon receives less energy than optimal.

If there is a different moon that receives more energy than needed, then a megastructure that covers the moon needs to be built. The purpose of the megastructure is to reduce the intensity of the energy from the star.

Another option is to build a ring world. Similar to the rings in the Halo game.

A seemingly good option will be to build a Globus Cassus.

If the gas giant has at least one moon that is suitable for terraforming, an artificial sun can be built which supplies the energy needs. This will work only if the moon receives less energy than optimal.

If there is a different moon that receives more energy than needed, then a megastructure that covers the moon needs to be built. The purpose of the megastructure is to reduce the intensity of the energy from the star.

Another option is to build a ring world. Similar to the rings in the Halo game.

A seemingly good option will be to build a Globus Cassus.