My first thought is that a day/night temperature differential may not be as important of a requirement as you apparently think. I suspect the added heating by your lights in the daytime, and not at night (coupled with the air conditioning) might be sufficient.
Evaporative coolers work by taking drier, outside air and evaporating water onto it, which absorbs thermal energy, cooling the air. The more humid the air, the less evaporation and cooling will occur, and at night, when outside temperatures typically lessen, the RH naturally increases.
If you put one in the grow room, it will boost the humidity, reducing the temp a bit, but that becomes self-limiting. They are mostly used for daytime cooling, to compensate for increased light levels.