You can buy them warm (we did, actually), but we took ours home, as we were short on time and just had a HUGE breakfast at Lulu's. Their signature breakfast is a huge chicken fried steak/chicken with gravy, eggs, home fries, and toast. Can you imagine scarfing down a giant cinnamon bun after that?
But that's ok. Even more than 24 hours later, the cinnamon bun was super moist, tender, and awesome. Being warmed is just a personal preference, it's just fine at room temperature. It's wrapped really well so it stays very fresh for a long time. The dough is yeasty (its how they get it so big), sweet and tender, and seems to have the unique property of absorbing moisture like a super sponge.
The bun is so large that they have to use a lot of icing, and so it tends to sit in a small pool of it. Because of its' sponge like properties, the bun soaks up so much moisture from this pool of icing that when you get to the bottom a day later, it's been transformed into ribbons of cinnamon sugar rock candy. A bit too much for me, but hey - it's fun to take a small nibble.
It's a long row to hoe
When the seeds that you sow
Grow by the wicked moon