Even after turning you need to be sure there are three things in place in your compost to encourage the bacteria that will generate the heat to get to work digesting what is left, Moisture (enough bit not too much), Nitrogen (enough but not too much), and air and in a 3 x 3 pile that will not be a problem and you need not add anything to "aerate" your compost pile. As with the original stack of material how it heats up depends on the ratio of C:N and the moisture and one of the reasons compost piles do not always reach the highest temperture after being turned is because that ratio is no longer there.

When we lived in short-season New Hampshire we had one huge pile that got anything and everything organic, from huge volumes of leaves to twigs to garbage to clothes to whole corn stalks to rotten pears to whole walnuts to my sister's many poor gerbils. Come Spring, once the ground had thawed and dried and we were getting ready to turn under last Fall's cow manure, we'd take one pile and fork it over onto the other spot, starting a new pile. What didn't fork was compost, or close enough. That went right onto the garden. No picky metering it out or piling it up, it just got spread and used, and we then had a (new) pile that didn't get touched (except for the piling-on and for fishing worms) for a full 'nother year. No turning. No worrying about ridiculous green-brown ratios or weed seeds. No thermometers. Just a totally simple, low work, and effective pile. Everything eventually rotted down. We just spread it around and got on with the gardening. In a way there are no bare spots underground, and roots will grow, inter-mesh, and find the nutrition the plants need. What I'm trying to illustrate is there's no need to store anything. Holding it back until you're ready to plant something in a particular spot does nothing for you other than make extra work or cost extra money. All it is (ALL) is adding back organic material you're removing by growing food and grubs. No magic. Use it now, use it all, and there will be more next year.

Here is a link to a great compost calculator, input your ingredients and obtain the C:N ratio. C:N should be 25-35:1 with 30 your goal. You really need the mix of carbon (brown stuff) and nitrogen (green stuff) for development of the decomposing organisms. The minimum size of a 'hot' pile is 3' x 3' x 3' which offers the proportion of materials to support the organisms and maintain moisture and temperature. Greater the 5' x 5' x5' should be the limit since it require more management action; beside being a heavy task in turning. ha ha C:N is the simplest means. The pile does need turning when a drop in temperature suggests. Turning mixes the ingredients to ensure all is exposed to decomposition. Your best resources are those available free. Grass clippings, kitchen wastes, garden wastes, manures, leaves, and straw are the easiest to work with without problems of odor and pests. A slowly built pile will not heat so well. Try building an entire pile with a proper 25-35:1 C:N ratio. You will see it heating up in days and shrinking in volume by the end of the week. Work the pile without further additions until finished. Monitor the heat, moisture and possible odors. Good composting. Dan Here is a link that might be useful: Compost Calculator

If you have finished compost now the time to spread it on your soil is now. There is no good reason to wait until spring to spread the compost you have now. Compost can be spread on soil anytime it is ready, finished, although few of us would do that when the garden has 4 feet of snow on it.