When it is hot and quiet, we also like calling at night to find responsive elk. Actually I like to do that anyway. Fairly often you can find them again in the early AM. Getting them to stay responsive in the daylight is the tricky part, when it is the hot and quiet time. I would also allow quiet elk the chance to come in to your calls. We aren't very good sitters and tend to keep on walking looking for ones that are in the mood to talk back to you. But we have had times when sitting for lunch or just when you find an area that seems like there should be something around, that after calling, if you given them enough time the curious quiet ones may work their way to you (because we always call a bit if we're going to sit for any amount of time). In the last few years we killed a couple that way.
Good Luck!
Mike