There are just too many twists and bends you need to make to current science, too many assumptions you need to take and on top of it, there is no evidence to show the hole exists. There are just wild speculations, what-ifs and pseudo science. I read this hollow earth theory like 10 years ago in another forum and thought that I would never see it again, but what a surprise.

Here is another such theory, maybe you should take a look at it as well.

Here is a description of Hanns Hoerbiger's Cosmic Ice Theory,

This is the story of a remarkable cosmology concocted by an Austrian
mining engineer, Hanns Hoerbiger. Hoerbiger was not only a mining
engineer, he was an amateur astronomer. Often, he would use a small
telescope to look at assorted celestial bodies, especially the Moon.
According to his account, early in this century, as he was looking at
the Moon, he was struck by the apparent brightness of its surface. He
had his first "recognition," that what he was seeing was ice, piled up
in blocks, producing the brightness and roughness he saw. Some nights
later, he had a dream and his second "recognition." He dreamt that he
was suspended in space, watching the swinging of a silvery pendulum,
which grew longer and longer until it broke. "I knew that Newton was
wrong and that the force of gravity stops at three times the distance
to Neptune," he concluded. This was the starting point for his Cosmic
Ice Theory.
This theory he worked out, in collaboration with a schoolteacher named
Philipp Fauth, in a giant book called {\it Glazial-Kosmogonie}. Here
is what it said: Once upon a time, there was a supergiant star in the
direction of the constellation Columba. A smaller star, dead,
water-soaked to the core, fell into it. It was heated up, vaporizing
the water, and causing a great explosion. The fragments of this
smaller star were spewed out of the supergiant into interstellar
space. The water condensed out into ice, forming giant ice blocks. A
ring of this ice formed, as well as a small number of solar systems.
This ring is known to us all as the Milky Way. Among the solar systems
that formed was our own, with many more planets than exist today.

Its stable by even force of gravity pulling. Then somehow got some mechanism make it float.

In nature best coolent is water and air .. And in caves there always water flowing with a slight breeze going through a duck or hole or passage way. As you can see in all the picture of caves. But as the case of hollow earth, the hole at the north and south could serve as cooling vents as both pole is very cold. As you know when hot air rush out, cold air goes in.
As we breath, cold air in and we puff out, hot air comes out. 

Read this about cave air system..

Air Flow in the Caves

Are the caves so cool because there are air conditioners inside them? There are a large number of visitors every year who ask that question. It surprises them that during a hot summer day the caves are a comfortable 17 degrees Celsius. During a cold winter day the surprise is that the caves are so much warmer than outside, a cozy 17 degrees Celsius. The caves stay close to the same temperature all the year round. The reason is that the surrounding rock is quite massive and an enormous amount of heat is needed to change its temperature. As air flows through a cave it comes in contact with the wall and, depending on the time of year, either warms or cools and hence ends up an even 17 degrees Celsius. Most caves exhibit the same phenomena although the temperature that they stabilise at will vary depending on what the average temperature is of the area they are in.

Understanding about the stable air temperature in the caves helps to understand why there is always fresh air despite large numbers of visitors passing through the caves. As visitors pass through they exhale carbon dioxide. If there was no air flow the carbon dioxide would collect in the cave and eventually it would become stifling. It would also start to corrode the formations. Fortunately we are helped by the fact the hot air rises.

During the winter months the air inside the caves is warmer than that outside. The air flows up and out of the cave. Since there are several entrances to the caves, the air flows out of the higher entrances and sucks cold air in through the lower entrances. The cold air that is drawn in is then warmed up, flows through the cave collecting the carbon dioxide and replacing it with oxygen. Eventually the air floats up and out through an upper entrance. The cycle continues, replacing the stale air.

During the summer months the opposite happens. During these months the air inside the caves is cooler than outside and hence it sinks and flows out a lower entrance. This draws in warm air through an upper entrance and hence another air cycle is created. Since it is very rare that the temperature outside will be exactly the same as that inside the caves, there will almost always be an air flow occurring to flush the caves of stale air.

Other atmospheric conditions will also contribute to air flow. Changing air pressure is a significant factor, especially where the cave only has one entrance. Think of a cave as being like a big plastic bottle. If you blow into a bottle the air inside will compress and assume the same pressure as that outside, i.e.. inside your mouth. As soon as you take the bottle away from your mouth, the pressure outside the bottle drops and a small rush of air occurs coming out of the bottle. Returning to the cave, air pressure is always changing. If the air pressure outside the cave increases, it forces more air into the cave. As the air pressure drops, the air that is stored inside the cave starts to rush back to the surface, causing a breeze.

Breezes are one way in which cave explorers find new caves. As they crawl around inside a cave they try and sense gentle breezes. Sometimes they will light a candle to see if the flame flickers in a breeze which is too faint to feel. If they find a breeze it often means there is a passage nearby that connects to other passages that are large enough to contain lots of air that responds to changes in air pressure.

dot this have major effect on our weather pattern since the air volume inside the hollow earth is so big, and why the two opening did not melt all the ice on both pole, since the sun is always shining inside the heat coming out of the hole will be constant all the time.