Because of super advanced, 200 million year old alien technology of course.
It was created by the Nuwali:
The Nuwali are one of the oldest intelligent races in the Universe, they achieved high levels of technology and devlopment millions years before most species.
So their super advanced tech trumps any logical argument as to how a tropical rain forest could possibly exist in the middle of Antarctica.
But, it's surrounded by a massive ring of volcanoes. So you could reasonably (not really) assume they produce enough heat in order to sustain the tropical climate:
The Savage Land is a tropical region surrounded by volcanoes deep in Antarctica, created over 200 million years ago by the alien Nuwali as one of several planetary "game preserves" for the mysterious godlike Beyonders.
When Earth's continents shifted circa 50 million BC, the Nuwali augmented the Land's volcanoes to preserve its tropical status.