This time of year, (while it doesn't say where you are, so I am assuming) but garages get very very hot, and a dog crate in a hot garage is going to be worse.
If you have a valuable flock, or will suffer a decline if you lose some birds, then you are right to quarantine. However, I might be misunderstaning the issue, but I think your quarantine might kill the bird. If I thought the bird was healthy, I would just add her to the flock. But I have a small flock, and while I would be darn crabby if I lost the works, it is a reasonable risk to me. If the hen was not healthy, I would not bring her on the place.
Introducing one bird can be very hard on the said bird, you might want to take a bird from your flock, and introduce her to the new one...... this is a way to kind of cheat on the quarantine by only risking one bird. If the flock bird stays healthy, it is reasonable to assume the rest of the flock will too, and you don't have to wait 30 days. You should probably wait 2 weeks though, then you introduce the pair to the flock, and each has a friend to share the abuse.
Don't know your set up, but I think heat might be a big problem.
Mrs K