Ralph, I believe the reason rivers like Big Q, Puntledge, and Campbell have been left open during closures is because they are heavily hatchery augmented flows/have kill fisheries. It's the same reason the Vedder was left open for the last summer closure (along with the Thompson). The reasoning behind keeping systems open was not due to water temperature. If it was, leaving rivers like the Stamp open would have been a drastic failure, as they often reached into the mid 20's (the Stamp was 24C and still open).
That being said, I do believe the Big Q does draw water from deep in the lake. It should stay relatively cool. I've never gone there in the summer to take water temperatures to confirm however, and ByteMe above would have a much better understanding of that.
Horne lake, although I've never fished it, does have very large cutthroat. My buddies who fish it say they are often hard to find as they move lots. If you're limited to shore, I'd target creek mouths in the evening. The creek out by the caves is a large one and may be a good starting point. As ByteMe said, the lakes will be getting warm by then. I'd advise to fish in the morning or evenings, and don't hold fish too long in the shallow/warm surface water for pics, etc.
Cameron lake may be another one you check out. I know people do well there from shore along the campsite end, and at the creek mouths. Again, Cameron will be warm, so keep that in mind if catch and releasing.