I hear that Jupiter and Saturn emit more energy than they receive from the Sun. This excess energy is supposedly due to contraction.
The book Jupiter: The Planet, Satellites and Magnetosphere, edited by Fran Bagenal, Timothy Dowling, and William McKinnon has, in its third chapter, the text: "[Jupiter] is still contracting at a rate of ~3 cm per year while its interior cools by ~1 K per million year."
The chapter does not give a specific source for that, but the chapter has an extensive list of references. I believe that the subject first came up in 1966 in a paper by Low who measured the infrared heat flux to be 1.9 times the incident solar. I was under the impression that this has been measured, but I was unable to find a direct reference to this; at this point it is likely to be a model and that's the amount required for the observed level of heating. One early paper that modeled this is by W.B. Hubbard in the journal Icarus, published in 1977 under the title "The Jovian surface condition and cooling rate."
