The best time to treat your fence is before it goes up in the first place. Apply the treatment to all the boards and posts before you install them.
If your fence is already up, wait until you get a dry day with plenty of cloud. Ideally, look to work in a calm day so that wind isn’t an issue.
If it’s too windy, you will end up leaves and debris onto your wet fence.
Hot sunshine will dry out the treatment too quickly and could make it streaky, and it makes for tiresome work and you want to take your time.