Saturn is an almost entirely gaseous planet, in the sense that most of its mass is hydrogen and helium. But only the few hundred miles nearest the visible cloud layers are actually gaseous as in the normal sense. As discussed in The "Surfaces" of the Outer Planets, the atmosphere increases in density as you go downward, and within a few hundred miles of the cloud tops, is as dense and incompressible as a liquid. It is not a true liquid, as it is far too hot to condense, and has no surface tension, as a liquid would; but for most purposes, the boundary between the easily compressed gaseous atmosphere and the nearly incompressible gas/liquid is the "surface" of the planet, and divides an essentially gaseous exterior from an essentially liquid interior.
This page briefly shows/describes the overall structure of Saturn (immediately below), and the conditions in that part of its atmosphere which we can more or less clearly observe (at the bottom of this page). When I have time, I will discuss both topics in greater detail; but for now, this "place holder" will have to do.
(Lunar and Planetary Institude, NASA)
A NASA model of the interior of Saturn. A gaseous atmosphere (shown in light gray), a few hundred miles thick, rapidly compresses under its own weight to the density of a liquid. From this "surface", the dense liquid/gas (shown in gray) compresses still further, over a distance of twenty-five thousand miles, until some of the electrons are forced from their atoms by the extreme pressure, and wandering freely between the hydrogen atoms, cause the normally non-conducting material to act like a molten metal (shown in dark gray), known as "metallic hydrogen". Deep in the interior, a core of various ices (shown in brown), perhaps as large as but ten times more massive than the Earth, is compressed to a dense crystalline structure, despite central temperatures in excess of twenty-five thousand Fahrenheit degrees. Not shown, because of its insignificant and unknown size, is a central core of rocks and metals similar to those found in the Earth, compressed to structures far denser than those inside the Earth.
A typical graph of the properties of Saturn's atmosphere. In this graph, zero altitude is chosen as the top of the troposphere, which is known as the tropopause, and is also the approximate location of a thin haze which obscures our view of the regions below. In other, otherwise similar graphs, the height at which the pressure is one bar, or equal to that at the surface of the Earth, would be chosen as zero altitude. In the lowest part of the atmosphere, the troposphere, temperature rises at about two Fahrenheit degrees per mile, from over 300 degrees below zero at the tropopause, to just above the freezing point of water ice at the bottom of this diagram (and far greater temperatures, further down). Although this temperature gradient is less than for Jupiter (which has a five degree per mile gradient), it is adequate, given Saturn's lower gravity, to make the lower atmosphere "neutrally stratified". This means that it is on the borderline between convective motion, which carries heat up from the interior, and lack of such motion. Hence, as in our atmosphere, this region is at least occasionally mixed by vertical motions, which leads to its designation as a troposphere, or "sphere of mixing".
The gradual change in temperature as we descend causes a change in the kind of ices which make up the various cloud layers. The high haze and the bright layer below it are primarily ammonia ice, but ammonium hydrosulfide dominates at greater depths, and still further down, water ice is presumed to be the primary cloud component.
As shown at the right of the graph, pressure also increases downward, doubling about every twenty miles. This is almost seven times further than required to double the pressure in the Earth's atmosphere, because the light hydrogen gas which makes up the atmosphere expands outward far more than the heavier atmosphere of the Earth would, under similar conditions. On the Earth, temperature increases a little less than 20 degrees per mile, for a little over 3 miles, while density doubles, so the temperature increases about 60 degrees while the density doubles. On Saturn, temperature increases only about 2 degrees per mile, for around 20 miles, while density doubles, so the net temperature increase is about 40 degrees while the density doubles.
As for Jupiter, the source of the heat in Saturn's lower atmosphere is the heat stored inside the planet since its formation, 4.5 billion years ago, plus a little heat added by gravitational compression as the planet cools, and by radioactive decay of heavy elements in its deep interior. But while Jupiter, with a substantially higher temperature gradient, and slightly larger size, must have central temperatures in excess of 50,000 Fahrenheit degrees, Saturn, with a smaller size and lower temperature gradient, probably has central temperatures of only 20 to 25,000 Fahrenheit degrees.
Finally, it should be noted that although in this diagram, temperatures appear to remain low in the "upper" atmosphere, at great height (hundreds of miles above the "surface"), as in the case of the Earth and Jupiter, Saturn must have a thermosphere with kinetic temperatures in excess of 1500 Fahrenheit degrees.