For a good quality third (or later) flush many aspects are important, but one of the most important is the temperature and also the time taken for the third (and subsequent) flushes.
The third flush must be allowed enough time to develop. " Heating up" a third flush to an air temperature of 18oC accelerates growth, but costs half the production and leads to quality loss. If the air temperature is kept at 16oC, the mushrooms grow much slower, so small pinheads also have more opportunity to develop. At higher temperatures growth stagnates.
A big disadvantage of a colder temperature is that the third flush takes much longer. If the second flush is all picked on a Friday for example, then the third flush can be expected on Saturday a week later, or even on Monday.
The planning must be examined closely and any delays avoided from the start of the cultivation cycle. Try to already harvest the first flush on a Saturday. Ensure the intermediate flushes are not too large, maximum 2 kg/m2. Finally, but not unimportant, do not allow compost activity to diminish, particularly during blow down.
Mark den Ouden, C point