Why does a compost heap get hot?

Because microorganisms are respiring — breaking down organic matter and releasing energy as heat, exactly as your own metabolism does, but concentrated in a mass large enough that the heat cannot escape as fast as it is produced.

The sequence. When fresh material is added, bacteria that thrive at ordinary temperatures consume the easily available sugars and starches. Their activity raises the temperature, which favours thermophilic bacteria adapted to heat, which work faster still. A well-built heap reaches 55–70°C within days, holds it while the easy material lasts, then cools as the remaining material becomes harder to digest and fungi and invertebrates take over the slow finishing work.

Why the heat is useful:

It kills weed seeds and many pathogens, which is the practical reason gardeners chase a hot heap. Sustained temperatures above about 55°C do most of this work.

It speeds decomposition dramatically — weeks rather than a year.

What a heap needs to heat up:

Volume. Below roughly a cubic metre a heap loses heat faster than it makes it. This is the single commonest reason a heap stays cold, and no amount of activator fixes it.

The right carbon-to-nitrogen balance, roughly 25–30 parts carbon to one of nitrogen — in practice a mix of "browns" like dry leaves, cardboard and woody material with "greens" like grass clippings, kitchen waste and fresh weeds. Too much brown and nothing happens; too much green and it goes slimy and smells of ammonia.

Moisture like a wrung-out sponge — dry material stalls, saturated material goes anaerobic.

Air, since the thermophilic process is aerobic. A heap that smells foul has gone anaerobic and needs turning.

Turning, which reintroduces air and moves the outside — which never got hot — into the middle.

Cold composting still works, just slowly and without killing seeds. Most domestic bins are cold heaps, and that is entirely fine.