I've always heard not to water your lawn during the day and that the fine water droplets will evaporate before it is absorbed by the lawn (either in the air or while sitting above ground). But how bad is it? Is there a direct correlation to the temperature outside?
The answer to the question is do not water your lawn during the heat of midday. Watering at night will eventually lead to Fungus on your lawn. The best time to water your lawn is in the early morning between 4 and 8 am. It has time to soak in to the soil and do the lawn good. Watering in midday is wasting water. It evaporates quickly. Twice a week should be enough. Make sure that you can put a half inch of water on your lawn each time you water. Put out a rain meter to measure amount of water.
I can answer the evaporation portion of the question. The most important factors to consider are:
1) the relative humidity of the air about your lawn
2) and the temperature of the water itself.
All the other factors will be constant for your lawn or are not correlated with day or night in general. (For instance, wind will hasten evaporation, but it can be windy in the day or at night in most locations.)
At night, air temperature is lower than during the day (usually!), which means the temperature of the water is likely to be lower, which means evaporation is slower. Additionally, lower air temperature means lower water vapor pressure in the air, which means higher relative humidity, which means slower evaporation. So all things considered, water on a lawn evaporates more slowly at night than during the day. (And that matches common sense. Whew!)
The gardening question is will the slower evaporation of watering during the night make watering at night better for your lawn relative to the amount of water used. I don't know for sure, but I believe that is correct with one exception. Too much water in the soil can cause plants to be unable to absorb nutrients and can cause root rot. If you flood your lawn at night, it might cause problems. But if you water at night, you should be able to use less water to get the same results than if you water during the day.
About a quarter, according to California Drought Preparedness:
Water early in the morning or late at night, and avoid watering during windy times of the day. By watering during the day, you can lose as much as 20 to 25 percent of your water to evaporation from heat and wind. And during the heat of the day, water droplets clinging to grass can cause the sun to “burn”the individual blades. Set sprinklers to run at night between 9 p.m. and 9 a.m.
Because of humidity there may be little correlation with temperature alone but this depends upon location (eg see Template:Climate chart/How to read a climate chart - using precipitation as a surrogate for humidity.)