Jupiter's core is hot, but not hot enough for fusion or it would still be burning today (albeit on the "low" oven setting). The Sun is hot enough for fusion. I'm not sure how much the heat difference is, but it's got to be at least that much...

Jupiter does radiate excess heat - more than it gets from the Sun - but this is left-over heat from its formation eons ago it is still slowly radiating. Earth is likewise still radiating excess heat from formation but only a few extra degrees more.

Those are great pics - I've saved them.
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"If they can't picture me with a knife, forcing them to strip in an alley, I don't want any part of it. It's humiliating." - windsock