They have recently softened their stance on caffeine to appear more rational and relevant
I'm not sure what would count as recent. As far as I know it's been clearly taught that Coffee and Tea were the only drinks officially against the Word of Wisdom. Mormons have been drinking coffee substitutes like Postum for a long time (like great-grandparents long time).
As for caffeine specifically, some local leaders may have interpreted things more strictly, but I have never seen any official church statement saying that it's against the Word of Wisdom.
What this means is that drinking hot peppermint tea is forbidden
It's actually just black/green teas. Herbal teas are fine. A drink being cold doesn't necessarily make it OK (eg. cold frappuccino is still against the Word of Wisdom), and being caffeine free doesn't make it OK, such as decaf coffee (also against the Word of Wisdom).
As for Jolt, Bawls, energy drinks, guarana, etc. it comes down to a principle of not letting the body be in control of the spirit. As such, we are taught to avoid addictions of any sort. So if you drink Jolt sometimes and it isn't addicting to you, that's fine (besides it being pretty gross...). If someone else finds themselves needing that can of Bawls to get going every morning, then maybe they need to get off that addiction.
I'm a Mormon, and my caffeinated beverages of choice are Guarana and Barq's root beer.