that was also my understand. the actual time shouldn't matter.
The time you temp should be consistent for your chart to be the most accurate. I think a lot of people who have babies who don't STTN still manage to see thermal shifts, but if your chart is full of a ton of open circles, FF will be less likely to be able to accurately pinpoint O (as will the board).
So if your LO wakes up fairly consistently at the same time in the middle of the night, you may want to consider temping then, if you've had 4+ hours of solid sleep time.