Just above freezing is perfect such as 40ºF which will keep the tree dormant over winter. So the greenhouse should be perfect. If it's put in a warm area, the tree will come out of dormancy too early and grow thin spindly growth that is very weak. Just keep the roots from freezing because if the roots freeze in the pots it is usually bad for any tree or plant and can kill it. You could also put the pot in a hole and bury the pot and then mulch around the tree and pot but this would be pretty risky since the plant is so young/tender right now.
They are hardy down to zone 6b or 7a (-5 or 0ºF)
They are deciduous and drop their leaves in late fall following the first hard frost.

Several of these are doing well in Denver at two different sites and have tolerated -10 F. with no dieback. I've heard water should be tapered off by this time of year.

Cacau

Interesting,i'd not heard of this tree. I see its in the Bignonia family and has large flowers.

Thanks so much for the info. Since they are still so small I'll keep them in the unheated GH this winter but will get them in the ground next year. It's such a pretty tree when in bloom. Hopefully I'll be able to grow these to blooming size. We get our share of cold winter temps but I'm sure it's warmer here then Denver though we don't get the insulating snow that they do.
Karyn

They seem to have a strong tendency to be multi-stem so be prepared to wrestle with them if you want "trees." One of them here grew from a two-foot plant to 3.5 feet in its first year after transplantation, and bloomed modestly over about six weeks, so I think you'll be successful in seeing yours flower.

Cacau

Karyn, just be aware, when/if you do get them in the ground that a snow cover is very insulating. If you have doubts about your desert willows doing well, you might look for a sheltered spot, but NOT one that warms up in the early spring, so the trees don't break dormancy too early. Many plants will survive fine under snow, while they have trouble being exposed to the warm/cold cycles of a winter with no snow. I can remember growing up in VT that some years the forsythias would bloom only on their lower portions - the snow cover had melted early, or not come that deeply - and the buds had frozen higher up the shrub.

As an alternative there is a hybrid (actually a cross with another species altogether) which might be a better choice.

Chitalpa

~Chills

Here is a link that might be useful: Chitalpa

I'm considering a desert willow (bubba) this year, but am not sure where I want to put it in my already established garden. I want to be able to move it around from spot to spot to see how much shade it will throw in relation to other full sun perennials in my garden. The one I'm thinking about purchasing is about 5' tall already, and I would transplant it into a large pot. will I be able to over winter it in the pot outside if I have to create it's own new bed?

I moved from Tucson Arizona to Cedar City Ut and brought with me seeds from the native Desert willow as well as burgandy. We planted the seeds in 2013 and have a yard full of them.......as do my neighbors who wanted some after seeing the blooms. We hit -19o one year and the trees came back beautifully. I think they will be smaller trees here because the growing season is shorter.....but they are tough! I was afraid that the weight of the snow on them would break the branches, but again they didn't have any breakage. biggest problem that I see here is that they are invasive. That is ok for me...but could be alot of work if you want a neat garden. still a hummingbird favorite!