Most fish see no problem with a couple point in either direction on temp.
But a small point of designing the whole tank might be missing. To get air to go into or out of a closed space, we have to have a second opening for air. So when we lay a small fan on the top to feed air through an opening that fits tight enough to hold the fish, we also need to do something for the second opening. I find one quick easy way to do this is to stick a pencil under the tank lid so that it doesn't close and leaves just a crack all around. This is enough to let air pass but not fish!
When I think of controllers, I find two main reasons for using them. The primary reason for me is the way heaters tend to stick full on when they fail. Adding a controller to the heater is very good as it will shut things down if the heater fails. I've lost three tanks of fish and never want to do that again so some effort/cost is okay with me.
Inkbird controllers are great and do a wonderful job.
My review here: Review- INKBIRD temp controller
But I also run enough tanks that I flinch at buying $40 controllers for that number of tanks. For a way to get past the price with a bit of DIY work, I often go this way to get controllers for both cooling and heating :
Wiring a cheap digital temperature controller
It all comes back around to what we each need to do to adapt things to fit our own tank and situation. I just added a new LED light to this tank and found it required yet another change to keep the temperature in range. Since this is a fish room and not a display tank, this works for me.
A small computer fan laid on top of the open lid will drop it several degrees and into the good range .
While the Inkbird controls it to perfection. set point to 78.0 and both heating and cooling are off at 78.6.