As for Methuselah, it's difficult to say for certain what happens to a gas giant after 12 billion years. The giant planets in our own solar system are actually still cooling. Jupiter, in particular, is known to emit more energy in infrared light than it receives from the sun. This is because of a process called Kelvin-Helmholtz heating, and it means that Jupiter is actually shrinking by around 2 centimeters each year. Over the course of a human lifetime, this is barely noticeable. But Methuselah is over 8 billion years older than Jupiter.
Curiouser and Curiouser Yet other pulsar planet is, somehow, stranger still. PSR J1719-1438 b, discovered in 2011, is believed to be made up mostly of carbon, crystallised into diamond. It's technically an ultra low mass white dwarf star, which had most of its mass stolen by the the pulsar it orbits. The remnant has no more mass than Jupiter, making it more planet-like than star-like.
ANALYSIS: Shedding New Light on a Pulsar Mystery
Because of this unusual history, PSR J1719-1438 b is considered a planet. In fact, it's the densest planet ever discovered, with intense pressures found below its surface which would cause carbon to crystallize. This sounds beautiful, but unfortunately for future sightseers, the gravity at the surface of this strange world would be enough to crush any visitors instantly. Provided they could survive the radiation from the pulsar, that is.