Re: It always amazes me...
Cuckoo!
Any information like that will be worked out on the basis of the observations that can be made and what we know about physics. It'll have been written up and published so it can be checked by everyone else working in the field.
You could have just googled it to find out how they worked out the wind speed, but no, better pull that tinfoilhat on tight.
https://science.nasa.gov/universe/exoplanets/5400mph-winds-discovered-hurtling-around-planet-outside-solar-system/
"try taking an infrared measurement off of a speck of dust drifting in front of a raging fire, from a mile away."
Without an atmosphere in the way, that's a technical challenge, but not impossible at all. With, say, 10,000x magnification*, that's like taking a picture of something 10x the size of a dust particle (so, say, 0.1-1mm across), from 5 feet away. Obviously, with an infrared filter on the camera, a picture _is_ a temperature measurement, so all you need to do is then look how bright those pixels are on your image.
[*This is not actually how space telescopes work. But it's good enough for the purposes of debunking that nonsense.]