In general, wort temperature at the low end of a yeast's range, during the early stages (first few days) of fermentation, promotes a clean lag phase, during which fewer byproducts are produced while the yeast are reproducing.
Increasing the liquid temperature towards the top of the yeast's range during the middle to end of fermentation, promotes full fermentation and clean-up of many of the byproducts produced earlier.
This,
I'll add that I think of the fermentation as a multi-step process:
1)Lag phase-Pitching to hour 18-24
2)Active Krausen phase- Day 2-6 marked by vigorous activity and krausen
3)Waning Fermentation phase- Variable timing but marked by lower activity while fermentation finishes
4)Conditioning phase, yeast cleans up then flocculates
Generally the temp is allowed to increase slowly from 1-4 then at the end of 4 you bring the temp down. But you can run all sorts of temp profiles to achieve different results.
In Phase 1, much of the yeast character of a beer is developed (which will be different for each type of yeast), the degree of this character can be changed by pitching at higher or lower temps. lower temp= lower yeast character, higher temp= more yeast character.
In Phase 2, attenuation is occurring, you can promote the speed an efficiency of this by increasing the temp. Yeast character is still being developed though to a lesser extent so the higher temps will cause a change in this flavor profile. lower temp= slower fermentation and lower yeast character, higher temp= faster fermentation and more yeast chearacter.
In Phase 3, the very last bit of sugars are being fermented. Higher temp here can cause the yeast to ferment out sugars that would have otherwise been left unfermented, resulting in higher attenuation. Very few yeast derived flavor changes occur from raising temps at this stage relative to temp changes in the previous stages. Lower temp= lower attenuation, higher temp= higher attenuation.
In Phase 4, The yeast clean up esters, diacetyl, sulfer containing compounds ect. It makes sense that a warmer temp here would promote this as well but I generally just let this happen at whatever ambient temp is. This part happens over a 2-3 week period and honestly its been my experience that this occurs effectively at a range of temperatures and it is really more about time than anything.
Then cold crash, I lumped this into phase 4.