When I first heard that cayenne was supposed to speed metabolism, I'd been drinking this and similar concoctions (hot and cold) for years as a decongestant/expectorant for colds, flus, and chronic respiratory illness.
I'd drink the hot lemon/cayenne at home, and I'd add cayenne to Crystal Light at work (or I'd make a pitcher of cayenne lemonade at home and would fill a large water bottle with it).
If there were any metabolic effects at all, they were so small as to be unnoticeable. I didn't lose weight any faster drinking cayenne/lemon concoctions (whether the concoctions were cold, hot, sweetened, unsweetened...) than when I wasn't drinking them.
Although it doesn't work (for me, at least) for weight loss, it is absolutely an amazing decongestant/expectorant. To this day, if I get a bad cold or a sinus infection, I make a big pitcher of cayenne lemonade (I usually drink it cold though. It works faster hot, but it tastes better cold - it just doesn't work for weight loss either hot or cold).
It can decrease appetite though, especially if you drink a glass before meals. I've also noticed that when I eat extremely spicy food (even though I love it) I'm more likely to eat less, and find myself satisfied sooner and less likely to eat until uncomfortably full.
And maybe that's why I've never noticed a difference with the cayenne lemonades, I'm already eating capsaicin-containing foods quite regularly.
If it does have any metabolic effect, I suppose that means I would have weighed a lot more than 400 lbs if I didn't love spicy food so much.