I recently rode my bike along the Mt Vernon bike trail and it had really nice coverage of trees to keep it cooler. There were many runners and walkers out enjoying the path and multiple spots to get on and off.
Roosevelt Island is nice, with a short sunny section on the boardwalk. From there you can lengthen your run (if it's not closed after a flood) along Potomac Heritage Trail and head northwest to Potomac Overlook Park - roughly 3.5 to 4 miles one way. Portions run parallel to GW Parkway in the sun, though. But Potomac Overlook is another nice. Or Turkey Run or Scott's Run if you like steep inclines here and there!
The trails at Rock Creek Park are almost entirely in the shade! I swear it's a few degrees cooler in there. I actually got chilly when I dipped down into the park after a hot, sweaty bike ride through the city. Here are the trails I tried most recently: http://dcoutdoorlife.com/rock-creek-park-bike-hike/
Depending upon your exact location, it might be a bit of a drive, but the Torrey C. Brown Rail Trail (aka North Central Railroad, or NCR Trail) in Baltimore County is really nice. It parallels the Gunpowder River and extends into York, Pennsylvania. It is mostly shaded, and even has a section with exercise equipment stations alongside.
one or more gifts or other benefits from the co-op.