ok, so here's what you do.
82 F is too high, period. I'm really surprised your roots are as white as they are at those temps, it must be a testament to your sterilization or luck
. Root rot will hit you at that temperature at some point in your grow unless you can get it down to at least 75 F and preferably between 68-72F.
Solutions: First, i can see that your res is not covered by any reflective coating. Go to the hardware store, grab some reflectix. It is attic insulation that looks bassically like aluminum foil sandwiched around bubble wrap. It reflects like 99% energy. Then, roll it out, make a sheet large enough to cover your lid, cut holes for the net pots and replace them with it covering the lid. Make it hang over the sides like and inch or two, or to the walls if you are in a small space, since this will block more light from hitting the sides of your res. Take the holes you cut out and cut a slit in them, then place them arround the base of the stems of your plants to cover the rocks and reflect more of the energy.
This will DRAMATICALLY lower your temperatures, by probably about 10 F. The reason is right now you are spraying the water onto the underside of a dark plastic lid that is directly being heated by your lights, and if you stop this then the only method of heat exchange your res will have is through the sides with the ambient air. It will still heat up over time, but i guarantee this is the cheapest most reliable way to get yourself into the safe zone. If you can raise your lights put the res on a couple bricks or 2x4's, just get it off the floor. Heat from the floor will be conducted slower if there is air insulating ur res from direct contact.
Second, start freezing ice in bottles your res looks a bit small for 2l bottles, so maybe smaller ones or even ice packs. Swapping in one 2l bottle lowers my 25L res by 7-10F. It will then rise back over 12 hours or so. I keep my temps between 64-74. If you are dilligent in watching the temps and are generally at home then this can be a solution to avoid a res chiller.
Third, definetly get an air stone. I have run my aero setup with and without one, and i've settled on adding one mostly for redundancy. At your temps though, every little bit of dissolved oxygen you can get in the water will help. In my setup the roots have at least 9 inches to hang in the air, and they only start to grow into the res at a late stage. Your res looks kind of shallow however, so i would guess the majority of the root mass will in fact end up submerged if you are vegging them in that setup. I have found with my aero plants that once the roots hit the water the plant starts building all it's roots there and starts to develop an underwater root ball which can end up being huge. With your system, i don't think i'd be comfortable without an airstone, and it certainly can't hurt, can only help. Cheap as hell too.
Finally, don't cut the roots unless they start to get slimy. It doesn't hurt the plants too much; in my system i have to untangle a bunch of dwc plants every month and they loose some roots in the process, but i've never even seen stress in the new growth as long as lots of roots are left. So you could cut em and you'd be fine. But there is no reason to in my opinion because ultimately you really have to solve that temp issue, and if you do then they will be able to sit in the water just fine. Get the temps down and grab a 10$ pump from a pet store.
Gl!
. 3 out of 4 people living in this house have no idea that I'm growing and I would like to keep it that way. So I can't just add a bottle of ice whenever I feel like it. I can only work on my setup at random times (which makes things difficult). I will definitely give your first suggestion a try however, it can't hurt. As for the airstones, would they add any heat to my water?
