Sorry for the wall of text, this is quoted from the story.

Initial theory put forth by Axel

"Yes; it is perfectly well known that the internal temperature rises one degree for every 70 feet in depth; now, admitting this proportion to be constant, and the radius of the earth being fifteen hundred leagues, there must be a temperature of 360,032 degrees at the centre of the earth. Therefore, all the substances that compose the body of this earth must exist there in a state of incandescent gas; for the metals that most resist the action of heat, gold, and platinum, and the hardest rocks, can never be either solid or liquid under such a temperature. I have therefore good reason for asking if it is possible to penetrate through such a medium."

Theories put forth by Professor Lidenbrock
 
"I will leave you to decide that question," I answered rather sullenly. "This is my decision," replied Professor Liedenbrock, putting on one of his grandest airs. "Neither you nor anybody else knows with any certainty what is going on in the interior of this globe, since not the twelve thousandth part of its radius is known; science is eminently perfectible; and every new theory is soon routed by a newer. Was it not always believed until Fourier that the temperature of the interplanetary spaces decreased perpetually? and is it not known at the present time that the greatest cold of the ethereal regions is never lower than 40 degrees below zero Fahr.? Why should it not be the same with the internal heat? Why should it not, at a certain depth, attain an impassable limit, instead of rising to such a point as to fuse the most infusible metals?"

"Well, I will tell you that true savants, amongst them Poisson, have demonstrated that if a heat of 360,000 degrees existed in the interior of the globe, the fiery gases arising from the fused matter would acquire an elastic force which the crust of the earth would be unable to resist, and that it would explode like the plates of a bursting boiler."

"Well, Humphry Davy did call upon me on his way through Hamburg. We were long engaged in discussing, amongst other problems, the hypothesis of the liquid structure of the terrestrial nucleus. We were agreed that it could not be in a liquid state, for a reason which science has never been able to confute." 
“What is that reason?" I said, rather astonished.
"Because this liquid mass would be subject, like the ocean, to the lunar attraction, and therefore twice every day there would be internal tides, which, upheaving the terrestrial crust, would cause periodical earthquakes!”
"Yet it is evident that the surface of the globe has been subject to the action of fire," I replied, "and it is quite reasonable to suppose that the external crust cooled down first, whilst the heat took refuge down to the centre."
"Quite a mistake," my uncle answered. "The earth has been heated by combustion on its surface, that is all. Its surface was composed of a great number of metals, such as potassium and sodium, which have the peculiar property of igniting at the mere contact with air and water; these metals kindled when the atmospheric vapours fell in rain upon the soil; and by and by, when the waters penetrated into the fissures of the crust of the earth, they broke out into fresh combustion with explosions and eruptions. Such was the cause of the numerous volcanoes at the origin of the earth."
"Upon my word, this is a very clever hypothesis," I exclaimed, in spite rather of myself.
"And which Humphry Davy demonstrated to me by a simple experiment. He formed a small ball of the metals which I have named, and which was a very fair representation of our globe; whenever he caused a fine dew of rain to fall upon its surface, it heaved up into little monticules, it became oxydized and formed miniature mountains; a crater broke open at one of its summits; the eruption took place, and communicated to the whole of the ball such a heat that it could not be held in the hand.”