Hot composting takes less time due to a universal law of nature which defines how fast chemical and biological reactions occur.
What is This Law?
Rates of chemical and biological reactions are determined by the Arrhenius equation which is often abbreviated into the Q10 formula.
What Does it Mean in Terms of Speed?
The rate of reaction (composting) doubles for every 10°c increase in temperature. This holds true for composting up to 75°C. Above 75°C, composting bacteria die and the rate ceases to increase. With like for like material and other conditions; a heap at 60°c composts x32 times faster than a heap at 10°C ambient (ie UK annual average). A rough approximation: it if takes 12 months in a 'cold' heap, then it would take 12 days in a 'hot' heap.