Phase II is called pasteurisation, but that is only its middle act. First comes pre-pasteurisation conditioning: the compost is levelled to a uniform 45 to 48 °C and held in the 45 to 52 °C band for two days. Then pasteurisation, a short controlled peak that kills insects, nematodes and competitor spores. Then post-pasteurisation conditioning, back to 45 to 48 °C until the ammonia is gone.
Run the tunnel as one long hot period instead and you get compost that is clean but still full of ammonia, and the spawn dies in it.