We would have to monitor it for an awfully long time, hundreds of millions, if not billions, of years.
Pallidin is correct. Gravity tries to compress large planets causing massive internal pressure and heat at the core. The processes of conduction and convection will cause some of this heat to rise to the surface. This happens, to a lesser degree, with the gas giants in our solar system. The surface of Jupiter receives more heat energy internally than it does from the sun.
Not entirely true. Planets (even gas giants) form in a slightly different way to stars (including brown dwarves). Stars form from the gas in a nebula. Planets form from the dust left over after the formation of the stars, so although on the surface a gas giant may appear like a failed star, having enough mass to form a large atmosphere of left over hydrogen, it's core is rock and very different from that of a star.
By measuring the wavelength of infra-red light it emits.
And I thought they just had a Long Thermometer.