See this link from the Miss Pond Manual - I would say read pg 37.
Thee best time to eradicate fish from a pond
for restocking is late summer or early fall.
Water temperatures are at their highest at this time,
and the weather is usually dry, allowing easy draining.
Killing the fish at this time reduces the time between
the kill and the restocking, which minimizes
the chance the pond will be contaminated by unwanted
fish before restocking.http://msucares.com/pubs/publications/p1428.pdf