From your description, you need more greens. Yes you can add weeds. Most weed seeds get killed in a hot pile. Some survive a hot pile, your decision weather to use them or not. I do cover mine with black plastic bags held down with stones otherwise it would become too wet. I may uncover in the heat of summer if I want to let rain in. Regarding the mouse, It will not like a hot pile or one that is turned regularly. Don't worry about it. Add some greens. Scrounge up some lawn clippings. (not yours since you should be mulching them back into your lawn) Toss in come cheap dog food. Rabbit food will really heat up a pile.
Bill Hill

Adding small amounts of kitchen scraps and weeds over several weeks will likely not make your pile heat up. Also, the soil and already composted manure you put in only absorbs heat and produces none. You really don't have to add those to a pile that is on the ground in contact with soil. It doesn't hurt though.

You might be surprised to find that mice live in your lawn and around your place all the time. Our cat catches them in the suburban lawn. You just happened to see one, but your compost is not a county-wide vermin attractor. It's just nature's cleanup crew doing its job.

Does your pile have the proper level of moisture? If it's too dry, it won't heat up, either.

I agree that the likely reason is not enough greens at once, though.

Of course, as you've noticed, it will all rot eventually, just sometimes more slowly than others.

Mice definitely prefer a rather drier environment. I used to see them in my finishing bin rather than the first bin, where the compost was more done and dry to facilitate their tunnelling.

Thanks everyone! I think I did have it too dry, so I've added some water and given it a good stir. I am searching for more greens to add beyond our kitchen scraps. I know stuff is breaking down in there, but I really want to see it heat up!

I want to echo tox on a couple of points. Mice are already there, and nothing cools my pile down faster than dirt. If you want it to heat up, you're going to have to hit the scavenge trail for materials---I tell you, it's remarkably easy. If you're shy, gain access to a child and make them come with you so you can call it "Earth Day" activity. My neighborhood is thick with bagged grass clippings on trash day, my neighbor took a green spell of saving her peeling for me, and of course anyplace that sells coffee has grounds.

try to get manure and/or coffee grounds, they are probably the easiest green sources. and as mentioned before, make sure it is moisturized properly. if the pile is big enough it can not be to wet (i soak my pile and it gets up to 130), think about it, good wet materials provide a setting perfect for microbial activity: darkness, moisture, food....don't forget oxygen, i used to not understand the importance of compost aeration, it is a big deal!

I've got two finished piles waiting for planting time. They both were slow (last summer and over the winter) to turn into black gold.

NOW...I'm working on a 3rd pile I'd like to go faster and see some of that heat you're talking about.

I understand what needs to go in there, but how much? How large of a "biomass" of greens/browns is needed to enable to heat to start. Size of my bin is 3x3x3, but it's only about 8 inches deep. Do I fill it all at once? I don't know where I'd get that much green material all at once. Do I add gradually more greens & browns and when it's full, then expect to see heat? If so, then what do I do with the new kitchen scraps I'm accumulating? I never did notice my old piles heat up by "by gum" I've got two 3x3x3 bins full of compost. Maybe I should just shut up and do what I've done before? HELP! Suggestions?

In a pile or bin that gets things added gradually as described by teequiltbarbie probably will not heat up. It will however still make excellent compost. If you want to see it heat up, then save up some leaves or other browns and then when you come into a huge find of grass clippings mix them all together and place them in your bin. Some cheap dog food or rabbit food would be another source for greens if you don't mind paying for stuff. I have read that a 3x3x3 ft. bin is about minimum size for a hot pile. Although I know that pile of grass clippings left on the ground will heat up by itself. Your 3x3x3 should be fine.
Bill Hill

Probably not enough Nitrogen in the mix. Whether there is enough or maybe too much water depends on your weather the last several months. Adding good rich garden soil is not necessary and earthworms are not significant digesters initially. A pile of material to compost can shrink simply as air is displaced and an 18 inch pile of material is not quite enough volume to get the bacteria that will digest the material really excited.
Any once living plant material is good in a compost pile, some people will tell you no "weeds" because they do not understand how things grow. If they said no "weed" seeds, and maybe no "weed" roots that might be understandable, but then of course it is simply easier to say no "weeds". Manure is a good addition to compost, but it does need to have a lot of Nitrogen still readily available, something aged manure does not have.
The link below will take you to a very good compost tutorial.

Here is a link that might be useful: Composting

I once added hot water to a pile that needed water, and I found that the pile was steaming big time a day or two later, tho the pile wasn't hot before I added the water...is that a bad practice? The steaming part of the pile looked a little ashy.

rosecats - I think the fact that the water you added was hot had nothing to do with the pile steaming a day or two later. No need to heat the water. In fact if you heat it too much you might kill microbes that cannot take the heat. Thermophilic bacteria make their own heat. The ashy looking area of the hot pile is a desirable fungus.
Bill Hill

Thanks billhill: that info helps a lot. I guess although I've seen it happen in my own piles (cold piles still work) somehow I thought a pile needed to heat up to make "good" compost. If not, then why do folks worry about heating up the compost.

I've read FAQ'S and know that it all will turn into compost eventually...but does it turn faster if it heats up. I'll just keep adding little at a time because that's how my supplies come to me.

I think people worry about their piles heating or not because many relate heating to fast or higher quality compost. It may be a little faster but no higher quality. But I have to say, there is something intensely wonderful about digging into the top of a bin full of working compost and seeing steam stream out on a cold morning. Stick your hand in there and feel the heat. Smell the moist earthy smell and then plunge you thermometer in and find the internal temperature in the 130's or higher. Um Um Um, that,s living. I think of my hot bins as if they were nuclear reactors, heating up inside. In fact the early nuclear reactors were called piles.
Bill Hill

Again, thanks, billhill. I get it. I bought myself a cheap ($1 store) pool thermometer just to try it and it, obviously, never shows any heat. SO...I guess I'm a cold composter. If I get lots of greens at one time (I have lots of browns waiting in a pile) I'll try to layer it, wet it and see what happens. One more fun gardening goal to set for myself. :)

Bill Hill, I gotta agree - I've heard many a time that slower/cooler piles are better, but I do love seeing that steam! Clear evidence of success, I suppose. Thanks for the info on the fungus.