Charlie, this is what I constructed last year, to use for rooting. In fact, I built two.
I keep them in my unheated basement, which lingers at about 50 degrees.
For light (and heat) I use a two-bulb, 4' t-5 fluorescent fixture in each, suspended from the rafters
with jack chain, and poking through the lid, and each fixture is suspended some 4" below the lid. This setup keeps the environment at 70-75 degrees, and fairly steamy.
I have to air them out everyday.
I also agree that you should add some ribs to that box so it won't bulge and blow apart.
Be extra careful with the light source. Make sure there's a drip loop below the fixture to keep
moisture from live parts, and keep the fixture a couple of inches away from the foamboard. That stuff is highly flammable
and noxious.
Get yourself a little fire extinguisher and a battery operated smoke detector, a timer, and you should have a three prong extension cord, plugged in to a GFCI outlet.
Set it to only run when someone's home for the first couple of weeks.
Don't hesitate to reach out to me if you want to talk more about your setup in private.