Yes. Both the Dyson Airstrait straightener and Dyson Corrale straightener have a feature which turns the straightener off after a set period of time. 

Dyson Airstrait straightener

The Dyson Airstrait will enter auto-standby after five minutes of inactivity when the arms are left open, or three minutes if the arms are locked. 

The LCD screen will turn off and you'll need to press the power button to turn the machine back on.

Dyson Corrale straightener

If the Dyson Corrale straightener is left unattended with the power on for longer than five minutes, the heated flexing plates automatically start to cool down. An alert will sound every 10 seconds and the Power button will flash. Pressing any button will re-activate your straightener.

Once a further five minutes has passed, the straightener will turn off completely.
 

YouTube

The Dyson YouTube channel hosts a vast amount of content that can support on this process. As well as those that provide tips on using, maintaining, and getting the best out of your Dyson machine. Simply use the on-screen search option or navigate through the playlists to start viewing these.