This is a latest addition after the rubberband fridge to currently ongoing series of compression-decompression cycle related inventions.
You may have noticed that, when we walk, we alternately compress and uncompress our shoes (soles, to be specific) with each step; This happens unintentionally as
our weight falls on the shoe which is touching the ground.
These shoes which are being proposed, will be just regular shoes except they will have additional side flaps similar to bird wings, which will cover both sides of each shoe. These flaps will be made of thermally insulated material. Purpose of these flaps is to preserve coolth (or heat as applicable) that has been building up in the shoe due to walking.
Lets first see, how these shoes can be used for cooling the foot.
There will be in all four flaps. Two per foot. These flaps, which are hinged at top will open like a birds wings when we put the foot down thus allowing (compressed and hence heated) shoe to cool off by convection.
When we lift the foot up off the ground, flaps will close; Shoe will uncompress hence be cooled; It will absorb heat from the foot in the process, thus cooling it.
This will be repeatative process. So as we keep on walking, shoes will keep getting cooler and cooler.
Good for walking in hot climate.
Now, what if you are walking in snow in mountains, say like trekking, you will need shoes that heat up themselves.
There will be a mechanical switch, which will reverse the timing for flaps. Simply toggle that switch. Now flaps will remain closed when the shoe is compressed as we put our foot down. They will open, the moment we lift the foot off the ground.
You got the idea.
Note that heavier the person, and/or softer the shoe, more effective heating/cooling is.