I have Stanhopea connata which I bought at an auction last year. It has grown well, but not bloomed yet. It came with almost no roots and bare root, and now the roots are visible from the sides & bottom of the basket. Yay!
After removing a few of the plastic net basket "bars" I lined it with a thin layer of sphagnum, then planted the orchid in a small orchiata bark mixture with perlite, tree fern and charcoal to keep it sweet and open. Seems to be working.
I'm growing in a converted sun room in th winter where the night time temps are about 55-58 F. It gets good air movement and catt levels of sun.
So I suspect you can grow this in a sunny window easily. No greenhouse needed.