Why is the exoplanet HD 131399Ab so hot? Recently, a fascinating triple-star system with an exoplanet has been discovered (arxiv). 

I'm very surprised about the temperature of the exoplanet: it is roughly 850 kelvin, even though its orbit is ~82 AU away from the main star (~1.5 $M_☉$), and >250 AU from the other two stars. The planet itself has ~4 jupiter-masses.

Why can such a planet be so hot, for instance compared to Jupiter? I would have expected it to be very cold because it loses a lot of energy via radiation (that's actually the reason why the group discovered it via direct imaging), and it does not get much energy from its stars.
It's a giant planet and it's young. p.3 of the paper you reference gives a likely age of 16 million years.

The heat arises from gravitational contraction and it would be a similar temperature even if it were further away from the stars.

When a ball of gas contracts, the virial theorem establishes that half the gravitational potential lost is radiated away and half heats up the gas.

Jupiter would also have been much hotter in the past and even now emits more radiation than it receives from the Sun. The rate of contraction (and hence the planet's luminosity and temperature) decreases as the planet ages.

Direct imaging surveys for giant planets deliberately target young stars for this reason.