I do feel that personal-climate-control clothing has potential in our future world of more climate extremes. Some kind of backpack with a fluid pump, heater-cooler unit, and battery. Cooling/heating fluid gets pumped around a suit. Inductive charging via pads on the posterior, as long as your seat is part of the superchairger network.
It will if the air is moving sufficiently fast over it, e.g in combination with the fan cooler. Or you can have a bucket with a mix of water, ice and salt, and point the fan to blow over it (we did this in army and it actually works fine as a poor man AC alternative).
Even if it doesn't evaporate, it will still absorb body heat, briefly. Similarly, if you are in a humid area, sitting in a bath / some body of water will help a lot. Don't underestimate the heat capacity of water.
It reminded me of the body suits which people need in Termination Shock (2021)[0]. Written by Neal Stephenson, the same dude who wrote Snow Crash. Can recommend Termination Shock, very interesting, global story about climate change and the involved politics etc.
These body suits do exactly what's being described in these comments. Wearable packs which regulate humidity, temperature etc.
I could see that happening for heat: hot water bags are amazing, and being able to "wear" one occasionally on the upper back (using some improvisation with an empty backpack to keep it in place) has been one of the few things I consider a benefit of WFH. But cooling? Sure, the technology is doable but won't you get a very huge mess with condensation?