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Buit if the links I found are accurate about Saturn’s core temperature, and since Saturn is assumed to be mostly gaseous, the core temperature , if around 7000°C would ignite the gaseous atmosphere and melt all liquid or ice into gas, ignote them...

Saturn should be on fire if this is true about the core temperature.

Same with jupiter. AND Uranus and Neptune

Saturn should be on fire if this is true about the core temperature.

It radiates that heat away. One of the links I found said that Saturn radiates away more heat than it gets from the Sun. There must be huge convection processes going on in Saturn where hot material from the core rises, radiates away its heat, then sinks back down into the interior. The cloud tops aren't on fire because they do not retain their heat.

Perhaps a better way to think of it is in terms of heat flux, how much heat per second flows through a square meter on Saturn's "surface." Both the surface of the Sun and of Saturn are in thermal equilibrium: that is, they are radiating away heat at the same rate it's coming up from the interior. Otherwise, the temperature would be rising (or falling), and it is not. The Sun's surface has been at 5,400ºC for, what, billions of years? Saturn's surface is holding at -285ºF. One is fiery. One is ice cold.

The difference is, the Sun's surface is dealing with a massive heat flux generated on a massive scale by fusion at the Sun's core. The heat flux on Saturn doesn't come from fusion and is minuscule in comparison. Saturn's surface has no trouble dumping it off into space before it can build up.

But give Saturn the heat flux of the Sun and we can absolutely guarantee it would be very fiery surface indeed!