How hot a brown dwarf can be at the core?

[zed]

For example a sub-brown dwarf (having less than 13 MJ (Mass of Jupiter)) that can't fuse anything, like WISE 0855–0714

How hot it can be at the core? And how much time it needs for it's core to cool significantly? Like for example for the core to cool to 273°K (0°C) or to 373°K (100°C)

The same question for Neptune: how much time it needs for it's core to cool significantly? Now it's probably 5,400 K

thanks

[FraserClarke]

The core temperature is quite a strong function of the object mass. 13Mjup is the lower limit for sustainable Deuterium burning (when you get enough energy from Deuterium fusion to match the object's luminosity), at which point the core will be about a 0.5 million kelvin or so.  Unfortunately Deuterium is so rare compared to Hydrogen, even a 13Mjup brown dwarf uses all it's Deuterium up in a few million years -- which is why the 13Mjup 'limit' for brown dwarfs is stupid; but that's just my professional opinion on the matter

After that, it will start cooling. It depends what you mean by 'significantly', but the core of a 13Mjup object will only have cooled by about 1/2 (i.e. still >200,000K) over the age of the universe...