No, I think any sort of "hot house" or greenhouse is out of the question.
I planted the luffa gourds around the lattice that surrounds 2/3 of our
small back porch. (roughly 6' by 6') The only way I would be able to
enclose it would probably involve making it so we can't walk in the back
door at all.

Thankfully, the bone meal I applied, coupled with lots of pinching of the
terminal buds, seems to have made a remarkable difference. Now there are
about 18 hefty looking female fruits that look like they will all flower and
start maturing. If the one large fruit I have is the rule and not the
exception, then these things can grow half an inch a day! If that's the
case, I'm guessing most of these will mature. We are close to being smack
dab in the middle of a city of 1 million people, and it is always about 5
degrees warmer here than out in the country nearby. We also tend to get
about 10 to 14 days more of a growing season. (delayed frost - probably due
to all the warmth from the houses, etc.)