Biga

It all depends on whose book you're getting your information from and what people call a biga. A biga , to some people, is a very dense preferment of 50% or so hydration. Because there's so little water relative to the flour, the yeast doesn't grow as quickly as in a 100% hydration poolish. These dense bigas do expand and ripen, just more slowly.

Ciril Hitz' book, "Artisan Baking" is the only book I've ever read that suggests an overnight stay in the fridge for a biga. It's possible other bakers are in favor of refrigerating a biga, I just haven't read their input as of yet.

I've also seen books discuss bigas that are around 68-70%. That doesn't sound like a biga to me but their authors have credentials and a track record while I'm just a raggedy home baker.

Your best bet is to try the instructions out on a scale of one or two loaves because you have so little to lose. If it doesn't work, you'll be out of maybe a pound or so of flour. If the idea works for you, don't fix it and keep using it until it stops working or you want to try something new.

A biga is supposed to double in bulk, so you could, of course, let it rise at room temperature (I find it takes about 4 hours to rise at room temperature). However, when I make a biga I normally let it rise overnight in the refrigerator. I just find it more convenient this way.

Since I often use a biga in my breads, I make more biga than I need for a single baking and then freeze the extra. If you're interested in doing this, these TFL links will give you more info...

Freezing Biga for Future Use

50% Whole wheat Bread (The Frozen Biga Test)

As Postal Grunt says, it depends on whose methods you employ. I work a lot with bigas at 75% hydration, à la Peter Reinhart's "Whole Grain Breads", and those require refrigeration for "at least 8 hours and up to 3 days".

Karin