If you find the water at Windermere Lake too cold for comfort, head up the hill and check out Lillian Lake, a small wooded lake on the way to Panorama.
Lillian Lake is popular with anglers, but also makes for a pretty good beach as well. There are some hiking / mountain biking trails in the woods across the road from the park if water isn't your thing.
For picnicking, Lillian Lake has a couple of shaded picnic tables overlooking the lake, a fire pit, bench and put toilets.
Lillian Lake is popular, both with mountain bikers and with stand up paddle boarders, so this picnic site can be crowded on a hot day. However, the views, the warm water, and the great location make it hard to beat. If the beach in Invermere is too crowded for your tastes, I recommend checking this site out.