You can have RadioPublic stop playing after a set time. To do so on iOS tap the podcast artwork in the player controls, it's in the middle next to Home and Explore at the bottom of the screen. Tap the '...' in the upper right hand corner and there will a label "Sleep timer". Tap that, tap a time and RadioPublic will stop playing when the time limit is hit.
On Android there are several sleep timer apps available in Google Play which will stop audio after a set time.