Answer: I think you've started off in the right direction, you just need a little help. My first recommendation is a book..."Let ItRot" by Stu Campbell. It is a wealth of information for anyone interested in composting. Lots of tips on whats, hows, whens, etc. Compost piles are hottest in the center. To keep it cooking, all you need to do is turn the center out towards the edges and the cold material along the edges of the bin into the center of the pile.
For a compost heap to work efficiently you need the correct ratio of carbon to nitrogen (approx. 30 parts carbon to 1 part nitrogen). Don't worry--it doesn't have to be exact! We commonly refer to this as "green stuff" (nitrogen) and "brown stuff" (carbon). During late summer/fall we have an abundance of grass clippings, weeds, vegetable waste (green stuff) and fallen leaves, straw, cornstalks (brown stuff). Just remember, it's best to layer a bit of "green stuff" in between larger layers of "brown stuff"!
You need enough material starting out to form a pile at least 3' x 3'. Smaller piles may not heat efficiently. Also, by starting in the fall, weed seed becomes sufficiently moist to swell, freeze and be destroyed over the winter months.
There are all sorts of ways to construct your compost pile--a pile/heap, pit, container, ready made "composter", etc. There are many choices, each with advantages/disadvantages. I've had success simply taking some chicken wire (or hardware cloth) and forming it into a cylinder, then setting it right next to the garden.
Temperature does affect composting, but generally that refers to the temperature inside the pile. Different people use different numbers but I recommend you try to get your pile to reach a temperature of 90-140F inside the pile. Heat is generated as decomposition occurs and microbes go to work. This hot temperature range is favorable to the most efficient microbes...the ones that do most of the work. (You don't want a temperature much higher than approx. 158F because higher than that for prolonged periods can destroy beneficial bacteria and fungi.)
I'm really puzzled that you're finding ashes in your pile. Perhaps the ashy-looking matter is actually fungus, not ashes, because you excluded air when you covered the pile. At any rate, keep turning your pile and you'll have finished compost in no time at all.
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