If you can convince the neighbor to dig out the grey, soil scented, well composted manure off the bottom, that'll be the best for your plants. The fresh manure is far too nitrogen rich and will burn your plants. To produce the heat you want, you're going to have to make lasagna. The same neighbor with the horses also probably has a wet bail of hay they can't feed them. Take the wet bail, take the manure, and in a one foot raised bed, layer them thinly in alternative layers. The resulting pile should look like lasagna, being light (hay), then dark (manure), then light, then dark, etc. ending with hay on top, to keep the residual scent down. Also, any decaying plant matter will do if you can't get hay. Compost can be used to, but it's more potent so spread it thinner. Water in dolomite lime from above to maintain pH, adding just a dusting evenly over the top. And when I say water, I mean heavily and daily for AT LEAST two weeks. While in this stage, covering the beds with black plastic will solarize the forming soil. This means your bed will be heated by the sun and itself, and the high temperatures will destroy unwanted microbes, but won't get hot enough to destroy beneficial microbes and rhizomes. The raised humidity will also accelerate the decomposition process. The excess watering helps spread the lyme, encouraging decomposition- which makes more nutrients and micronutrients available, and allows the incredibly potent compost tea / lime mixture to leach into your subsoil, enriching and loosening the ground below for your roots. A two foot lasagna stack makes about six hyper potent inches of loam, but your roots will cut far further into the moist, pH balanced subsoil. Remember, two weeks of heavy daily watering should be enough time with well composted manure, but even fresh manure can be turned into brilliant soil with two months of patient attendance. Also, you won't need to till the bed. Stack more layers to cultivate stronger, deeper, more diverse soil between yields. Introducing worms isn't only cheap and easy, it introduces worm castings and aeration to your soil as well. Best of luck, you've got plenty of time until spring to grow your soil!