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It only goes anaerobic if its too wet and the heat dies off. If that happens, stop watering and mix fresh material into the center of the pile. You should always check your pile's core heat on a daily basis anyway. This will tell you if you need more moisture or if you have too much or if you need more carbon-based materials etc.
I would remove all composted materials and remix the non-composted materials into the new compost pile. If the hay is in useable condition, then why not reuse it?
In my opinion, if you're trying to heat your greenhouse by heating tubing that winds through your compost, you should either use copper tubing or aluminum. Aluminum is much cheaper by the heat transfer into the copper pipe is double from what you get out of aluminum. And plastic will give you 1/200th the heat transfer from the compost pile into a plastic pipe.