Since I haven't done an exbeeriment checking to see the effect temp control has on my beer I can't offer a definitive answer--but there are several "it depends" issues as well as my own particular answer.
Some beers simply won't work well at higher temps, which really limits what you can do. And as others have noted, fermentation raises the wort temp perhaps up to 10 degrees above ambient. My ambient is about 65 degrees but left to itself my beers will get to 70 to as much as 72 degrees while fermenting.
I started paying more attention to fermentation temperatures at about my 5th or 6th batch. It may be a coincidence but that's about when I started to produce beers I'd rather drink than what they serve at the local pub. Seriously; I sit there drinking theirs while thinking "I wish this were mine."
You might be able to test this using a swamp cooler. There's a thread in which that discussion is ongoing. That swamp cooler will likely drop your fermentation temps 5-7 degrees depending on how you do it. This would let you examine the role temp plays in your own brewing without spending much at all to test. And you can get more cooling out of it if you drip water onto the cooler and/or use a fan to promote evaporation.
https://www.homebrewtalk.com/showthread.php?t=593167
As to whether my beer is better with temp control? All I know--and I'm knocking on wood as I write this--is that since I started doing it, I've only produced one beer that I wasn't WOWed by, and that may be due to trying first-wort hopping without having accounted for the increase in bitterness.
People ask this question over and over here and the overwhelming response is to control your fementation temps. I can't recall reading a post from anyone where they say it doesn't matter. Do it.