For active decomposition of animal carcasses, compost microorganisms require a source of nitrogen (N) (dead livestock or birds), carbon (C) (straw, corn stalks, shavings, litter, etc.), oxygen, water and elevated temperatures.
An ideal C:N ratio should fall between 15:1 to 35:1. Oxygen (air) can be introduced when turning the compost. If proper moisture is not supplied, the organisms cannot survive. Ideally, moisture content should range from 45-55%, or wet enough when the compost is squeezed to leave your hand feeling moist, without actually forming drops of water. When all components are present in the correct ratio, the compost pile heats naturally, destroying pathogens and viruses while microbial activity degrades the carcasses.

Resources:
http://www.mda.state.mn.us/animals/animals/composting.htm
http://www.agnr.umd.edu/MCE/Publications/Publication.cfm?ID=35
http://www.bae.ncsu.edu/programs/extension/publicat/wqwm/psfact11.html
http://www.agnr.umd.edu/MCE/Publications/PDFs/FS717.pdf

By Josh Payne, PhD, Oklahoma State University