Does Jupiter emit heat? If so, is it enough to support life on one of its moons?
Jupiter doesn't emit large amounts of heat.
Jupiter is a planet, not a star. Although it is mainly Hydrogen it would need to be over 13 times its size to start any form of heat producing fusion reactions.
Jupiter however is massive. It heats up its moons through tidal forces. The innermost jovian moon IO is highly volcanic due to tidal heating from Jupiter and the other moons.
Jupiter's moon Europa has an oxygen atmosphere and an icy surface. It is thought that under the icy surface is liquid water due to tidal heating. It is possible that there is life in the oceans of Europa.