I have to agree with GA on this one.

While I will give you points for thinking outside the box, it's a no bueno.

You would be better off keeping your room temps lower if possible, maybe an A/C?. If that isnt an option you would be better off buying a nutrient chiller and running RDWC.

Option B: nutrient chiller. best to go pro and buy one if you plan to do hydro long term in hot conditions (along with an A/C).
If you make your own nute chiller DO NOT USE COPPER TUBING or any coppper components that nutes will be flowing through, as copper is poisonous to plants in very small doses.

To make a cheap nute chiller (in case $500 for a good one is out of budget) hook your buckets together RDWC style and pump your nutes through an aluminum coil that rests in a bucket of ice water.
The length of the aluminum tubing that is submerged in ice will determine how cold your nutes get. The longer the tubing that rests in ice, the cooler the nutes get. you can always cut the tube shorter and or put your pump on a timer. If you do this keep a hawk eye on your nute temps. This is not a long term solution, and its got its draw backs since your plants will all be getting the same nutes. Recirculating DWC can be a bit more of a challenge. just giving you options.
option C: since you're only using 2 gallon bubblers, you can set each of those inside larger containers and fill the larger containers with cooler water. try to keep your nute temps in the mid 60's for good levels of disolved oxygen. This is not something I would recommend as a permanent solution, but it could save your plants if it comes to it.

If it were me I would spend the money to get an A/C, and possibly a nute chiller. your plants will love you for it.

Hope this helps...