Giff Walters submitted this route description:
Thompson Peak (10,751') is the highest summit in the Sawtooth Range. There are four routes to the top of Thompson Peak with the easiest being class 3 (the South Couloir route). It is an extremely aesthetic climb with amazing views from the summit. From the Redfish trailhead it is ~6 miles to the summit with a gain of ~ 4200 ft.
From the trailhead at the backpackers parking lot cross the road and follow the Fishook Creek trail for about .8 miles to a signed junction (the sign will indicate Marshall lake). From here head north through a grove of aspen trees to the ridge top. Once atop the ridge follow it northwest towards Williams peak. Along the way you will pass the wilderness boundary sign - fill out a permit and continue on until you see a split in the trail. Take the climbers trail to the left, which brings you around the southern base of Williamson. Follow this trail until it ends at a hanging meadow in the basin surrounded by Williamson to your right, and Thompson in front. Continue up the meadow until you reach the beautiful high alpine lake at ~ 9000 ft which sits at the base of Thompson. From the lake keep heading up towards the headwall that forms the saddle between Thompson and Williamson. To surmount the headwall, navigate towards the side closest to Thompson. Here you will find a break in the cliff that will allow you to scramble up to the saddle with little difficulty (it also holds snow for much of the year). From the saddle traverse up and around the west side of the peak onto class 2 scree and talus. Follow this up and around towards the south side of the peak, here you will find a short couloir/gully that contains a bit of class 3 scrambling to take you to the summit (melts out early). At the apex of the couloir, go left and scramble up some ledges to find the summit block and register.