I often read about ramping up the temperature to increase yeast activity and attenuation towards the end of fermentation. I used to have some really funky tasting brews before I started strict temperature control throughout my entire fermentation.
Is there a general rule that after x gravity/hours the yeast have generated most of the flavours that a brew will have?
Generally, most yeast created flavors will happen in the first 72 hours. After that (in general) you can start ramping up. You can also wait 4-5 days to be safe.
It also doesn't hurt to start low, leave for a couple of days, increase, leave for a couple of days, etc. I usually don't increase it once I see krausen until the krausen starts to fall, but mosts ale yeasts say 65-75, but will ferment nice and clean down at ~60. This varies by yeast, but never hurts to start a bit low. Also, raising the temp a couple of degrees a day once gravity hits 1.02x will help it finish off and ensure a rest (especially if initial fermentation was very low, like 50s).
I don't think that there will be a time where fermentation is still ongoing, but that there will be no off flavors generated. As I understand it, what's going on when a brewer raises the temperature for a time during fermentation, they are allowing for the generation of some off flavors. It will either fit the style of the beer, or if enough of the fermentation is already complete, then any undesirable flavors will be muted.
Depending on the style, the yeast, and your recipe there probably is some point where you could raise the temperature without it adversely affecting your beer. I'm not sure exactly where that would be, but you could monitor the progress by examining the gravity and allowing the temperature to rise after some benchmark is reached between your your OG and FG.
That said, unless you're making some Belgian or farmhouse style I would probably avoid changes in temperature as much as possible, as the change in flavor would be difficult to predict. It's occasionally necessary to kickstart a stuck fermentation, but I would be reluctant to try it if I didn't think I needed to.
