Because air has a specific heat of about 1 kJ/kg*deg K, the air charge is only 3.8 C (or K) degrees cooler for the rich mixture compared to the optimum power mixture. This small difference has very little effect on knock or power output.

Richening up the mixture results in a slower burn, moving the pressure peak later where there is more leverage, hence more torque. Also the pressure peak is lower at a later crank angle and the knock probability is reduced. The same effect can be achieved with an optimum power mixture and more ignition retard.

If the mixture is ignited to early, the piston is still moving up towards TDC as the pressure from the burning mixture builds. This has several effects:

The pressure buildup before TDC tries to turn the engine backward, costing power.
The point where the pressure in the cylinder peaks is much closer to TDC, with the result of less mechanical leverage on the crankshaft (less power) and also causes MUCH higher pressure peaks and temperatures, leading to knock.

Many people with aftermarket turbos don't change the spark advance very much, believing that earlier spark creates more power. To combat knock they make the mixture richer. All that happens really then is that the mixture burns slower and therefore hits the peak pressure closer to the right point. This of course reaffirms the belief that the richer mixture creates more power. In reality the flame front speed was adjusted to get the right peak pressure point. The same result (with more power, less emissions and less fuel consumption) could be achieved by leaving the mixture at the leaner optimum and retarding the ignition more instead.