You know, I'd almost repost this question separately... My guess would be that it would totally depend on the bunny (that's great that they will neuter him...and like you, I like being able to "rescue" one). I know it's that way with cats and dogs...some shelter animals can make better pets...
I think just about any animal going from house temps to outside temps (if there's a big difference) should be transitioned gradually. I'm assuming there is a secure, cozy little nest area (lol..yeah, I know it's a rabbit rather than a chicken, but I don't know what you call the house area)...