I grew tenuifolia for years...until it simply got too big and I didn't want to deal w/trying to accommodate it any longer. It then found a new home w/a fellow OS member.
Personally, I wouldn't grow it below mid to upper 50's...I think, in the long run, it might not appreciate really cool temps.
When I got it, as a very young plant, I mounted it on a tree fern totem with the hopes that it would one day grow completely around the totem. After a couple of years of decent but not spectacular growth I decided it wasn't getting enough moisture on the totem so I put the totem in a 6" clay pot and back-filled the space w/lava rock and then I put a layer (fairly thick) of sphagnum in the top of the pot. I was able to keep it moister and it took off w/growth over the next few years.
In the summer - I would water nearly every day and the pot sat in a saucer of water. I tried to never let it get completely dry. Bright, catt level light. And then in the winter - I watered a bit less but I still watered it far more than I would any cattleya. During the winter it sat under the HO T5's...as close as I could get it w/out burning the leaves. After a couple of years it was growing like gang-busters but I still wasn't getting quite the number of blooms I thought such a large plant should be producing so the next summer I moved it to full sun in the summer. After acclimating it, of course. After the move to full sun (from morning until mid-late afternoon)...the blooms exploded.
My temps through this entire process - in the summer it got whatever mother nature threw at it and in the winter the lows were 58-60 and day time would typically be in the 70's somewhere. Before the orchids would go outside each spring the temps in the grow space can get well into the 80's during the day w/the lights so that was extra heat at this time of the year.
I looked and can not find a pic of it at it's best before I got rid of it but this one is in '13 when I decided I was going to subject it to more intense light and it would either give me more blooms or it would burn up.
You can see that it was well on it's way to absolutely engulfing that totem - you almost can't see it. It's a big totem too...18" tall, if I remember correctly. The pot is 6". That'll give you an idea of the size of the plant. It was blooming nicely and if you look closely you see there are still a good number of blooms that had yet to open. After the full sun treatment...it had 3-4X as many blooms. Totally covered! The smell was so strong that it was almost overwhelming on humid afternoons.
If I can find a later pic, I'll post it.
Hope that helps.
Almost forgot...as the plant grew up and out, I wired it onto the totem (sometimes wrapping sections toward the back in order to get it to cover the mount on all sides) so the growth was able to really grab onto the tree fern and the roots could take hold. That helped a lot w/making sure the whole thing was getting sufficient moisture.