I mean, yeah. But at some point the pile will become large enough to collapse in on itself from gravity and start fusion, I would imagine.
So, according to Cornell[don't know how to do a citation], "1,000 BTU per hour per ton" is a good heat capture rate from manure compost. Then, according to something called 'alternative energy geek' "the earth receives 82 million quads of Btu energy from the sun each year. A "quad" is one quadrillion British Thermal Units (BTUs) of energy."
So, to recreate that, we would need. Um. One massive shitload of compost to recreate that.