Yeah, spring and fall is the best typically. But temperature is not the key to what you're looking for. It's about what's floating around in the air. In fall and spring there is a lot of interesting bugs swirling around looking to propagate. By the time all the plants have entered their adult phase and have finished doing their things, so have the bugs. You end up with lots of lacto and other, less interesting microbes. The same is true for the back end of the growing process as well.
If you have an interesting growing season, try out other times as well! You might be surprised.
Get all your growlers together and try to collect from different places at different times and let them sit for a long time.