Why is the exoplanet HD 131399Ab so hot?
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.