Hello Kemer.
No need to go home and die (if that's a typical response on this board I may be done before I really get started).
Not much of Wyoming is very flat. Coming out of Cheyenne you're at 6,000' and climb steadily to around 8,600' over 30 miles. So nothing too bad but a 40mph headwind can make it seem like Everest. At the Summit you drop down from 8,600 to 7,200 in just a few miles, so keep it geared down and don't burn up your brakes.
Elk Mountain is a bump, but in the winter it can be the nightmare from hell bump. This time of year is fine though. You'll cross the Continental Divide twice in central Wyoming, west of Rawlins, as you cross the Great Divide Basin, but no hills to worry about on this stretch.
Between Fort Bridger and Evanston you cross the Three Sisters, three very long drawn out climbs that will make you tired of the sound of your engine sucking fuel at such an alarming rate. From Evanston it's mostly all downhill to SLC.
Hope you find this to be helpful.