I'm pretty sure that I did shut the door last night and lock it, because I doublechecked that I'd done it properly. Also, the room was quite warm: it would surely have been colder if it had been open all night. But I left the key in the lock.
When I came down in the morning, one dog bounced about then raced out enthusiastically through the open door when I opened the curtains. The other dog gave me a 'meh' face and settled down in his beanbag to wait for breakfast...
I think Az has learned how to turn the key. I knew he could open the Yale lock on the front door, but usually he doesn't bother. Obviously he feels he wants to pop out earlier than I am allowing. I may need to start getting up earlier. And remove the key and put it on a high shelf!