Does Jupiter give off heat?
Jupiter gives of relatively little heat.
It is thought that Jupiter has a very hot core at around 24,000C. Its cloud laters are quite cold at about -145C. So, Jupiter gives off only small amounts of heat.
Contrary to some opinions, Jupiter is not a failed star. It would have to be some 80 times its current mass to start fusion reactions.
Jupiter does have a strong magnetic field and also a strong gravitational pull. Gravitational tidal effects are constantly heating up Jupiter's moons. Io in particular experiences strong tidal heating and has active volcanos.