Gas giants can generate heat via the Kelvin-Helmholtz mechanism. It's oft-repeated that Jupiter actually generates more heat internally via this method than it receives from the Sun. Scale this mechanism up enough and you get into brown dwarf territory, with something that is effectively a star to a nearby observer (whether it is a star or not seems to be contentious).
A giant in "star mode" obviously emits vast amounts of heat and is agreed to have a very narrow, but technically possible, habitable zone in its own right, enough to be independent of any larger star it may be orbiting. How does this zone change in relevance as the giant decreases and it moves towards "planet mode"? Is it possible for an object to have a gentle enough "heat gradient" (?) that despite being cool enough that it doesn't visibly glow, it still noticeably warms its moons?
Example scenario: a superjovian/sub-brown-dwarf at, or just beyond, the outer edge of a parent star's main habitable zone. The giant has its own planetary moon system; on these worlds, the brightest object and dominant feature in the sky is the giant, which is cool enough to have visible stripes, no internal "glow" (the light would mainly be reflected sunlight), and to not vaporize any equipment sent into its upper atmosphere. I guess 300-500K.
How would the heat given off by such an object affect its satellites? Would it be able to raise their temperature by any significant amount - does a low central temperature on a massive object still cause a reasonably large zone of warming? How would/could this mini-zone interact with the zone of the primary star? (i.e. the sliding scale of "how far out can I move this before I have to make the giant brighter?" vs. "how far in can I move this before the giant's heat is completely overpowered?")
Allowing an extremely generous definition of "habitable" (e.g. a world that would have had a surface temperature of 150K is now merely Antarctic at the equator thanks to the giant).