I do not think that any physical laws are being violated, it seems to me that you are thinking in terms of a star being (for example) a coal burning stove. It radiates heat and then ultimately cools down. Looking at it in strictly mechanical terms is not consistent with a model which assumes that those mechanical requirements are changed under a situation which is dominated by electrical forces. I used the example of the Sun's temperatures: Corona (a low density plasma in glow mode at million degree temperatures, the photosphere (an arc mode plasma at around 6000 K) and sunspots (which are holes in the photosphere giving us a look at the layer below the photosphere at around 3000 K). Furthermore the temperature layering, between the corona and the photosphere, does not have very much if any temperature gradient. The corona is on top of the photosphere separated by a double layer with an enormous temperature difference between the two.
What can we say about the solar interior below what is observable? It seems (from the temperature gradient that we observe) that the interior as we move toward the center must be getting cooler. But in lieu of further information, the temperature, density, composition, etc. of the solar interior (and that of a brown dwarf too) is open to speculation.
So under the Electric Star hypothesis all the action is taking place on the surface. A nova under this model is not a mechanical explosion blowing apart a star, but rather an electrical event causing the star to throw off material, think of it as a scaled up CME, it may even signify a fissioning event. In the electric star model. We do not know at this time the nature of the interior of a star, this includes the density. Under this model the interior of a star or brown dwarf star is open to speculation, but it is definitely not analogous to a stove. [Remember, the EU challenges the notion that mass and matter are the same thing. Wal Thornhill has theorized that mass is a variable function of matter, with matter (the quantity of protons and electrons) being inviolable.]
The Saturn theory has to be viewed in the context of the electric star model, in this case a brown dwarf which is often called proto-Saturn. Of course this is highly speculative and there are several different and competing versions. Thousands of pages have been written on this and I for one am not going to attempt a summary.
My own view is that our ancestors were subjected to near extinction as the solar system was reordered and the Earth's land surface and hydrosphere were catastrophically altered. Trying to figure out exactly what happened and the cosmic agents involved is a work in progress. The Saturn theory, in some form or other, offers many intriguing explanations that seem to fit.
But it seems to me that your initial assertion of falsification by examination of the present temperature of Saturn (while worthy of consideration) is premature and in the context of the wrong paradigm.