unvented greenhouse -- any way to make it work for seed starting?

[habitat_gardener]

The good news is that I have access to a greenhouse this year.

The bad news is that the greenhouse is unvented. It's at a community garden and is used basically as a locked shed for tool storage, but I can start seeds there if I can find a way to make it work.

The question: is it worth trying?

It's convenient enough that I could possibly stop by twice a day (to take them outside and put them back inside), but I know from experience that it doesn't take much time for seedlings to fry, if I got there too late one time or skipped a day.

Shading the flat won't help, because (1) they need light and (2) a hot box is still hot if you add a sunshade.

If I place my flats at floor level (=the coolest spot, next to the glass), do they have a chance? A fan might help, but I don't know if there's electricity and I wouldn't want to leave a fan running unattended. But maybe there's a way to get some passive airflow?

I could buffer temperature swings by surrounding the flat with gallons of water, or placing a wall-o-water around a few containers, but will that protect them enough?

The alternative is to do what I've done before: start them outdoors in cold frames. If I start early, growth is glacially slow because nights are still in the 40s until May, and if rainfall is anywhere near normal, they also need to be protected from rainstorms. If I start late, then I end up getting plants for my main crop and growing only earlies and cherries from seed (and have only a short time to harvest them).

I'll probably end up trying a batch of seeds in any case, but it'd help to get some more ideas on how to make this work.