Storm did exactly the same the first night we had him, kept me up all night long with his howling. We kept him outside in the garage at night which was joined to the house with a conservatory, so there was only 1 door between him and the house....sounds a harsh place to keep him but it really wasn't.
I was determined to not give up and let him in the house when he was howling, so I just used to go down to him, spend a few minutes talking to him and stroking him, but 10mins or so after leaaving him again he would start howling...It was obvious he was doing it because he knew I would come and be with him again, but I couldn't leave him crying like that so kept going to him and just hoped he would get over it, and luckily he did..the next night he was fine.
He was always kept outside at that house as we were trying to sell and move at the time so he soon got used to it as he was always either in the garden or conservatory/garage....Now at this house he has his own bed inside the house, we have a second back door at this end of the house, with a very short hallway leading up to it, this is Storms back door, which also leads..(with dog flap)..to his own part of the garden which is fenced off from the rest...
...I think it is very important that a dog feels he has his own space/area to go to, no matter how small it is. It is nice and cool in the winter there for him, and in the summer we let him use the dog flap so he can go outside in the night if it gets too warm.
I think perseverance is the answer...
Is there another place to keep the cage, near a back door. It may be cooler and more comfortable for her. I don't think that is the reason for the howling but it may help her settle in quicker.
good luck, she won't do it forever I'm sure...