Nochawk has it right, elk will hit wallows and water holes throughout the day. Especially if those places are near bedding areas and in heavy cover.
I have sat all day several times and have been surprised to see how many animals come in during the heat of the day (from 10 a.m. to 3 p.m.)
Two years ago, I shot right under a big 6-point bull that came to a water hole at 3:00 in the afternoon. I wasn't in a stand but was sneaking down the trail to check out the hole when he came in. I put a stand up there last year and missed a decent 5-point the first week and then the hole went dry.
When the weather is hot and after the elk bed in the morning, I will go sit rather than head back to camp. Sometimes an early morning sit will be productive too. I have also sat in the evening, which is also productive. The way I see it, by sitting at water, you are adding tools to your arsenal and increasing your odds of being sucessful. I mix it up, but if I had to choose my favorite time to sit, it would be mid-afternoon til dark.
It has been my experience that elk wallow activity does not decrease a lot cool days (but it may decrease some), but the activity will decrease a lot if it the weather is rainy.
Some waterholes/wallows will dictate when you hunt them by their layout and location. One such spot I hunt is pretty much evening only, due to wind flows. There, I set up on the ground next to an aspen about 15 yards away, located downslope. I know that the elk tend to always approach this hole from uphill or side-hill. The evening downdraft usually starts flowing just before it's time for the elk to come in, which is perfect. I've never been busted in this early-season spot. Also interesting is that I've never seen a cow elk in this spot...always bulls in singles or pairs. Here's a young bull I let pass in that spot last year. He came to within 7-8 yards and hung around for a good while, never knowing I was there.
Then there are other holes I hunt where the winds swirl so much it's just hit or miss. Might as well hunt them all day or any time of the day, and just hope you get lucky WRT the wind.
Hunting these spots get much more spotty as September wears on.