Just a note- the Northeast Yellowstone streams open mid July to protect Spawning Cutt's. Every year folks show up too early.
I wear light weight waders but, also, will wet wade a lot in August. In July, definitely bring your waders. If you have a set of breatheables, they would be preferable. I would suggest wearing a wading shoe. Pools along the roads fill up early and you will have to walk in through sage, etc.
You probably would not be impacted by any "Warm Water" conditions that early in the summer. The policy IN THE PARK is to close stream at 2:00 to fishing when water temps get too high. If the streams are closed, you can fish the Clark's Fork of the Yellowstone or several hundred high mountain lakes to the east of the park. I will be the Campground Host at Crazy Creek campground in the Shoshone NF about 10 miles east of Cooke City. Stop by and I can point you to some lakes nearby. If you have a float tube, pontoon etc. with you, I can put you onto some Grayling. I have spent weeks out there fishing, without entering the Park
The discussion on the snowpack from the other thread is not to scare anyone away! I posted it so folks would be aware and have some other options available, if need be. I would hate to see someone show up for the trip of a lifetime to find they can only fish 1/2 days. The water levels in the northeast Yellowstone Area generally are determined by the amount of snow held in the Beartooth Mountains of Montana / Wyoming just outside the park. An ideal situation would be a large amount of snow with a late, long, cool spring , releasing water slowly. With the low amount of snow (by Beartooth standards), a very warm Spring could release what snow melt we have quickly, resulting in very low water levels for the rest of the year.
Shoot me an email firstname.lastname@example.org
if you want some NE section suggestions.