How warm will it stay at night? Remember to factor in wind when thinking about what kind of temperature buffer you have.

I would be a a little hesitant to put the warm lovers (tomato, pepper) out there too soon.

I would think you could put the cole crops out there now. In my small greenhouse I have lettuce and various cole crops and other cold lovers that sprouted outside. You could put the warm lovers out during the day and probably leave them out at night this week only, with the very warm nighttime lows predicted, but after that it could be iffy and they may be better off inside. We find that a tarp over the top of the greenhouse on very cold nights helps cut the heat loss somewhat. Good luck and remain vigilant! It's still March.

If you are up early the coldest part of the night is usually right around sunrise. you could check the temp in there then for a few consecutive days to see how it compares to the outside temp.
Usually I try to hold off until the night time low outside stays above freezing for a good week.
I'm also usually a little chicken to start so I'll choose a few "sacraficial lambs" of my seedlings and set them out first. If they do well, then I know I can put the rest out there.
Also, make sure it doesn't get too hot out there during the day as well. If we are forcasted for a sunny day, you might want to leave the door part open or open vents in the morning to ensure there is good ventilation.
I've lost more seedlings to over heating during the day than to colder temps at night.
I hope that helps you :)

I have a unheated residential greenhouse and would like any information that you may have regarding:
Safe time to plant seedlings
Recommendations on planting vegetable/flower seedlings
Night Temperature
Day Temperature
Last year I planted zuchinni and egg plants. Unfortunately the vegetable plants had beautiful flower blooms,but produced no vegetables. Help