ooops rented too small a place

3-panel folding screens, Japanese shoji screens, the media center cabinets that'll hold 52" screens. Tall free-standing bookshelves or cabinets, with things like MDF fiberboard panels in between. Ikea and similar stores have all kinds of room dividers, some expensive, some relatively not, which since they're not built-in, you can take down and take down with you to your next place.

get some sheets and a staple gun and staple them to the floor joists to provide a ceiling of sorts.Or get some foam insulation boards (the white, blue, or pink kind)at Home Depot, paint them, or cover with fabric, or graffiti art them if that's your thing. You can likely get them in widths that'll wedge firmly in between the joists (or cut them to fit with a utility knife). They should stay up with just a friction fit, since you're not loading them heavily. they should make it more livable, quieter, and probably help the temp. Hmm, I think the insulation foam boards come in 8 foot lengths, so you could use them to wall off the space too, since they'd likely reach from the floor to the joists, unless you have a really lofty basement.

Well it could be a liability issue having people live in the basement. What state are you residing in?

especially if there is no window...

At my first duplex I needed a divider. I took small cup hooks and screwed them into the ceiling. I then took some light material and sewed little plastic rings on (you can find them in brass too...probably silver as well) and hooked the rings to the cup hooks. I liked a little drape to it so the rings were a little wider spaced than the cup hooks were. Really inexpensive and it gave me the division I needed.