Is the plastic tucked REAL well all around the perimeter, and is it 'lined' with some weight (like Pressure Treated lumber or gravel or bricks or something) to keep it from 'lifting'? Is there any water collecting on the TOP side of the plastic? How large is the crawlspace? How many vents do you have? How large are the vents? Are your vents 'obstructed' in any way so as to prevent air from entering the space? What room(s) is/are ABOVE the crawlspace?
My first reaction (before you get a chance to answer my ?'s) is that the warm floor is 'drawing' moisture on to it. When the space cools, it condenses out onto your joists, and possibly on TOP of your plastic. Until you answer ALL my ?'s, I haven't more info to offer. However, I STRONGLY suggest you insulate your floor from the underside (inside the crawlspace.) Buy the Kraft-sided R-39 insulation, and install it w/the Kraft side facing the floor. You won't be able to staple the insulation in place as well as you'd like because this is normally done BEFORE the sub-floor is installed. You can still take your time and do your best to be sure the Kraft is 'covering' the underside of the sub-floor. Also, if you have any piping (cold AND hot), insulate it pipe-insulation-tubing (with the 'seam' facing DOWN so condensation can 'drip out'.) Wrap all your ventilation ducts with Duct Insulation, and tape in place with Silver Tape (NOT Duct Tape. The folks at the Home Center will tell you what you need. Just be sure to tell them what you're doing AND where you're doing your work.) After you've insulated, I suggest you either 'weave' some string on the UNDERSIDE of your joists (using Roofing Nails to wrap the string on as you go) or use some chicken wire to hold your insulation up. Let it 'hang down' so to speak. (Trying to staple it up there will be very hard and very time consuming.) You don't want the insulation to 'hang' from just staples which is why you want the 'string weave' or the chicken wire.
It's going to be a bit of back-breaking work because you're gonna be on your back a lot and holding your arms up. Get back to me w/some more info to ALL my ?'s and we'll go from there. Read through all the links at this site Moisture In Basements - Causes and Solutions to get a better feel. I think I've only added to it. My best to ya and hope this helps.