Thompson Peak is an easy summit from the Branham Lakes trailhead in the Tobacco Root Mountains of Southwestern Montana. Due to a short approach time and stable terrain, it can be a shorter day hike or one of a few easier scrambles/hike combined in a day. Several other peaks can be easily reached from this trailhead and potentially combined in one full day excursion. These include Leggat Mountain, Branham Peaks, and Long Mountain. On a clear day from the summit one can see many other peaks of the Tobacco Roots. As well peaks of the Madison, Pioneer, Gravelly and Snowcrest Ranges.
From the town of Sheridan Montana take Mill Creek Rd (FSR 111) from the downtown area. A hardware/grocery store is the last chance for food or beer. A sign for "Mill Creek CG 6 miles" is where you want to go. Follow this road for over 10 slow miles on a gravel road which may require 4x4 in some spots. It's not bad though. Clearance is not a huge issue so Subarus and other lower vehicles will fare ok. You will eventually come to the upper and lower Branham lakes. The Trail Head Begins at the southern end of upper Branham lake and should be easy to find. Look for a small bridge and parking off to the left.
The route is pretty straighforward, hike the steep alpine tundra from trail between the ridge connecting thompson peak and the trail. When you see a large cairn, this is point where you go off the trail and improvise a route to the summit. The picture above gives you an idea of how navigable the terrain is.