Having air temperature in high 70’s low 80’s isn’t a problem, that’s about where it should be with that type of light. Your water temp however should be targeted at about 68f. Best way is to use a chiller. It’s my understanding that you can get away with it being a little higher running a ton of oxygen and something like hydroguard, but you should check with some of the hydro guys for best information there.
I’ve always heard you can ruin water temps clean up to 78° but the amount of oxygen that needs to be pumped into the water when it’s that hot is astronomical.
It’s usually not to hard to keep an external reservoir at room temps which should be about 72° but normally, unless a chiller is involved, a good air pump will heat the water a couple more degrees, kinda fighting itself.
Dwc can be done without a chiller, but I don’t like running dwc at all without mine.
I do however like my reservoir to look like it’s at a “rolling boil” no matter the water temps. If I’m just getting tiny bubbles then I’m not getting enough oxygen