Why is my Xbox one and the adapter randomly shutting off?

Sonmy Xbox one will randomly shut off for no apparent reason. I suspect the problem is either the power brick or the Xbox itself, both could be subject to overheating.

The Xbox one doesn't make any noise before it turns off, it just completely goes off. The power bricks led also goes black and unplugging the cord from the brick and re- inserting it doesn't help. Even switching the cord that goes into the brick doesn't help, which leads me to thinking the cause is overheating. After a few minutes it does come back to life but starting up a game or something delivers the same results.