Hi Soni,
mulberries are more hardy than figs, Mulberries grow wild, like weeds, here in 5b
If planted in the ground they can survive the winter no problem. In your zone I think you could still plant the mulberry seedlings in ground this fall. mulch them a bit and provide rodent protection, and they should be fine.
the figs will not go dormant if your green house temps are in the 70's.
if the night time temps go to low, the trees might be damaged by the high/low cycling of temps.
If you keep the lows above 40 they will not go dormant.

Hello Grant,  Thanks for the info.  I'm flying by the seat of my pants in an unfamiliar zone 8.

,  Soni

Soni speaking on muleberry it depends on what type of mulberry plant it is as there are some that cannot take very cold temps.
Noir of Spain is one of them .
Illinois Everybearing inground can take very cold temps (below zero) i can attest here in Northern Illinois .

Q1  My little greenhouse temps aare in 70's F by day.  Is that too warm for 1 gal figs to be dormant?
YES.

Thanks Martin.   My mulberries are from seeds i planted "black Mulberry"  I think I'll protect then this winter.  They are less than 2 feet tall and thin as reeds. 

I still dont know what I'm going  to do with the green bark, 1 gal  baby figs. (less thana foot tall.)
Soni

Soni, I left my little figs (green bark) outside last night and they had a nice frost bath. After the next frost or two
which could be several weeks away, they will then go night-night in the garage for about five months.

I just thought the same thing as Martin.....
cold-hardiness ... depends of variety of mulberry.