In reply to TheDrunkenBakers:
Damping off is usually what gets them at this point, but it sounds like they just got shocked the other way. I'd grow them indoors, in a reasonably bright spot, but not in direct sunlight. You might find using a clear plastic lid or - if you grow them in pots - a clear bag to be useful. Obviously, using a slightly deeper pot would help to combat sudden changes in environment.
We've had some good weather lately, so have removed part of the greenhouse door and opened the vents - it was just getting too much in there.