It's a quirk of radio DJs to slip into "this hour" and "next hour" patter. When you're on the air, it's customary to say, "This hour, we'll have music from...," or "Next hour, we'll give away one hundred dollars to one lucky listener."
That phrasing sounds odd in any other context, however. I've never said to my cat, "Collette, later this hour, I'll give you some food," or "Next hour, I'll change the cat litter."