Today set a record for high temp here (83) for this date. It gets plenty hot here in summer, 100 plus. The outside air I was referring to was air from outside the growroom, so it could easily be air from inside your house, just not from inside the growroom. That's what I do, and it works tits... In fact, I don't recommend people use air from outdoors because the large temperature swings make mantaining stable conditions more difficult, plus the possibility of drawing nasties into your sealed growroom.
Let's take a worst case scenario, however, and you'll see this still saves cooling costs; let's say you bring 100 degree air in to cool your bulbs. Let's say that this air is kept separate (like it's supposed to be!) from all other air, including the growroom air. To do this properly, you'll want to use insulated ducting and perhaps hood blankets too, but unless you have some long runs it isn't required. You'll still come out ahead, I promise. If the temperature rise drawing that air through your hoods is 25 degrees, the air being pulled (never push air through hoods if you can help it!) out of the room is 125 degrees. Place the duct fan of your choice Downstream of the bulbs and as close to the exit as possible. For sure, insulate any ducting between the fan and the exit, it will be hot no matter what its temp was when it came in. The hot air then goes outside. You've still successfully gotten rid of most of the heat the bulbs are generating! The only thing left for the AC to cool is the radiant heat from the bulbs, which is what the plants are using to power their growth, and of course whatever else is in the room generating heat.
While this approach will not eliminate the need for active cooling, it will reduce the amount needed. As a bonus, the air used to cool the hoods should not pick up any smell on its trip, since it's supposed to be fully sealed off from the growroom air anyway, so there's no need for odor mitigation. It can be shut off when the lights are off, I suggest a 15 minute delay on startup and shutdown, so it allows the room to warm properly in the 'morning' and shed the residual heat at 'dusk'.