I would aim for a pile with lots of coarse browns, especially twigs or chipped brush, which had been thoroughly soaked in water prior to the addition of greens.
My rationale is:
* coarse materials have more loft, and allow a larger pile to remain aerobic without turning (since any heat exchanger would complicate turning)
*
wood holds a lot of water, meaning a less-thirsty pile, and a pile with greater thermal mass (for more throughput with less retardation of compost metabolism)
*
carbon from coarse materials isn't immediately available, and so the C:N ratio is effectively lower for the first part of decomposition, but remains more constant as decomposition proceeds
There are lots of options for a heat exchanger. You might build a large reservoir into the center of the pile, like a 55 gallon drum or an old hot water tank, or you could harvest heat through the walls of a garden hose, or maybe look into a salvaged heat-exchanger of some other type, if it doesn't contain heavy metals: home heating radiator, car radiator, the drained rear coils of a scrapped refrigerator...I
think it will really depend on what's most available.
"the qualities of these bacteria, like the heat of the sun, electricity, or the qualities of metals, are part of the storehouse of knowledge of all men. They are manifestations of the laws of nature, free to all men and reserved exclusively to none." SCOTUS, Funk Bros. Seed Co. v. Kale Inoculant Co.