Under decent conditions, with a relatively unlimited food supply, bacteria, yeasts, and fungi can double their numbers every twenty to thirty minutes, increasing geometrically: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1,024, 2,048, 4,096, etc. In only four hours one cell multiplies to over four thousand. In three more hours there will be two million.
For food, they consume the compost heap. Almost all oxygen-breathing organisms make energy by "burning" some form of organic matter as fuel much like gasoline powers an automobile. This cellular burning does not happen violently with flame and light. Living things use enzymes to break complex organic molecules down into simpler ones like sugar (and others) and then enzymatically unite these with oxygen. But as gentle as enzymatic combustion may seem, it still is burning. Microbes can "burn" starches, cellulose, lignin, proteins, and fats, as well as sugars.
No engine is one hundred percent efficient. All motors give off waste heat as they run. Similarly, no plant or animal is capable of using every bit of energy released from their food, and consequently radiate heat. When working hard, living things give off more heat; when resting, less. The ebb and flow of heat production matches their oxygen consumption, and matches their physical and metabolic activities, and growth rates. Even single-celled animals like bacteria and fungi breathe oxygen and give off heat.
Soil animals and microorganisms working over the thin layer of leaf litter on the forest floor also generate heat but it dissipates without making any perceptible increase in temperature. However, compostable materials do not transfer heat readily. In the language of architecture and home building they might be said to have a high "R" value or to be good insulators When a large quantity of decomposing materials are heaped up, biological heat is trapped within the pile and temperature increases, further accelerating the rate of decomposition.
Temperature controls how rapidly living things carry out their activities. Only birds and mammals are warm blooded-capable of holding the rate of their metabolic chemistry constant by holding their body temperature steady. Most animals and all microorganisms have no ability to regulate their internal temperature; when they are cold they are sluggish, when warm, active. Driven by cold-blooded soil animals and microorganisms, the hotter the compost pile gets the faster it is consumed.
This relationship between temperature and the speed of biological activity also holds true for organic chemical reactions in a test-tube, the shelf-life of garden seed, the time it takes seed to germinate and the storage of food in the refrigerator. At the temperature of frozen water most living chemical processes come to a halt or close to it. That is why freezing prevents food from going through those normal enzymatic decomposition stages we call spoiling.
By the time that temperature has increased to about 50 degree F, the chemistry of most living things is beginning to operate efficiently. From that temperature the speed of organic chemical reactions then approximately doubles with each 20 degree increase of temperature. So, at 70 degree F decomposition is running at twice the rate it does at 50 degree, while at 90 degree four times as rapidly as at 50 degree and so on. However, when temperatures get to about 150 degree organic chemistry is not necessarily racing 32 times as fast as compared to 50 degree because many reactions engendered by living things decline in efficiency at temperatures much over 110 degree.
This explanation is oversimplified and the numbers I have used to illustrate the process are slightly inaccurate, however the idea itself is substantially correct. You should understand that while inorganic chemical reactions accelerate with increases in temperature almost without limit, those processes conducted by living things usually have a much lower terminal temperature. Above some point, life stops. Even the most heat tolerant soil animals will die or exit a compost pile by the time the temperature exceeds 120 degree, leaving the material in the sole possession of microorganisms.
Most microorganisms cannot withstand temperatures much over 130 degree. When the core of a pile heats beyond this point they either form spores while waiting for things to cool off, or die off. Plenty of living organisms will still be waiting in the cooler outer layers of the heap to reoccupy the core once things cool down. However, there are unique bacteria and fungi that only work effectively at temperatures exceeding 110 degree. Soil scientists and other academics that sometimes seem to measure their stature on how well they can baffle the average person by using unfamiliar words for ordinary notions call these types of organisms thermophiles, a Latin word that simply means "heat lovers."
Compost piles can get remarkably hot. Since thermophilic microorganisms and fungi generate the very heat they require to accelerate their activities and as the ambient temperature increases generate even more heat, the ultimate temperature is reached when the pile gets so hot that even thermophilic organisms begin to die off. Compost piles have exceeded 160 degree. You should expect the heaps you build to exceed 140 degree and shouldn't be surprised if they approach 150 degree