Crawl space insulation
I don't have enough info to be too specific, but based on what you've said, I can get you started.
If the crawl's floor is dirt, yes, cover it w/6 mil plastic. be sure you DON'T go up the walls w/it. And put some bricks, or gravel, or something on top of the plastic all around the perimeter.
If your floor isn't cold, then the heat is doing 1 of 2 things. 1) Is it leaking from ABOVE into the crawl below? 2) Are you actually heating the crawlspace, accidentally or intentionally??!
If it's #1, you DO need to insulate. Use Kraft-side R-39 insulation, and install w/the Kraft side facing the WARM part of the floor. THen use Joist Hangers or chicken wire or some type of 'webbing' (home-made or not) to 'hold' the insulation up and to keep it from falling down. If it's #2, then fix the leaks in the ductwork or STOP heating the crawl. THEN, if the floor is cold, follow the idea in #1's answer.
Now, if the walls leak air, either patch them up appropriately or insulate. However, if water is leaking through those cracks, you need to FIX the leaks from the OUTSIDE first, then patch them up on the inside. Otherwise, you'll be revisiting this problem again and again. Assuming all the walls are not leaking, then you can insulate if you want. Hopefully, your patching of the cracks/leaks will suffice.
RE: Vents - It depends on what's done in your part of the country. I live in SE PA and we vent our crawls, year round. General rule: 1 vent per 150 sq ft of space.
My best to ya and hope this helps.
Jay J -Moderator
PS: God Bless America!
Put a vapour barrier on the floor , and lap it up the walls at least six inches, securing it with mastic. Overlap and secure all seams with aluminum tape or mastic (not regular duct tape).
If you decide to insulate the floor, you must vent the crawlspace, as it then becomes ouside the building envelope.
But in large parts of the US you have 3 or more months of the year where the outside air has a dewpoint of 60 or above. If that air is allowed into a crawlspace that is cool (both naturally from ground contact and from AC running in the house) the RH in that space will be very high and maybe even condenstation.
You don't want air inside the crawlspace. Seal it off.
If you use fiberglass batts under the floor check and see if they or the joist sub-floor are damp.
Do a google on Conditioned Crawlspace and Sealed Crawlspace.
Start at www.buildingscience.com