We use the current Disney version for running, if that tells you anything. I'm also wearing them to run a kids day camp in 95 degree heat.
Yep, you still get sweaty under them, but all of you is sweating (and luckily we don't have to wear them 100% of the time outside at camp). They are better than my other favorite masks (nicely fitted double cotton) which just absorb it all and cling to you in the heat.
They are more breathable than many masks, which makes them slightly less protective in both directions, so I would choose something else for truly close quarters or prolonged exposure (subway, airplane, drs office or any other waiting room), but they do pass the candle test.
When we went down in May and were wearing masks outside and inside on property, I figured out how to install a wire in the Disney masks. Big thing to know: the thread is all one piece. Snip it and the whole mask comes apart. So what I did was sew tightly around the hem on either side of where I was going to create an opening for my wire and THEN snip those stitches to slide it. Note: I use flat nose bridge strips (bought a pack of 100 last fall), and it's possible if you were using actual wire, you could just slip it in between the stitches and not have to cut at all. I haven't tried that.