Particle size of the starting materials. The smaller the size of the particles, the easier the food is for bacteria to use. If particle size allows too rapid bacterial growth, temperature will increase too quickly, become too high, and the oxygen will be used up, resulting in anaerobic conditions. The smaller the particle size, the more difficult it is for oxygen to diffuse into the material, and the more likely the pile will go anaerobic. Moisture must be adequate to let the organisms grow.
Nothing happens if the pile is too dry and no benefits can be maintained.
Probably the most generally useful compost would have balanced bacterial and fungal biomass, since then the plant would select for dominance of the microorganisms most beneficial to it. As broad a diversity of both bacteria and fungi would also be beneficial, regardless of what system into which the compost will be placed. If the manure is stinky, wet, or runny, reduce the amount of manure used. It is quite likely that this manure will be high in salts and will result in phytotoxicity. If your compost heated too fast, you have too much juicy, N-rich green stuff.