Why does room temp water evaporate good?
Evaporation occur at any temperature.
Will 90 degrees F water cool to room temp of 70 degrees F faster than water at 50 degrees F warm up to 70 degrees F room temp?
Actually alcohol at room temperature would be of the same temperature than water at room temperature. The difference between the two is that alcohol needs less heat to evaporate. If you wet either hand in alcohol and water, the one with alcohol will feel colder because it's removing more heat from you and faster. That's basically what cold is, the absence of heat.
The light bulb increases the temperature, and the higher the temperature, the faster evaporation occurs. The light bulb itself doesn't evaporate water. If you're using the old incandescent light bulbs, they will give off a lot more heat, and evaporate more water than an energy-saving bulb. It also depends on the distance between the bulb and the water, the surface area, mass of water, and time.