Because the only way for one side of the device to be cooler is for the other side to be hotter, this particular device must be positioned where the heat from the hot side will dissipate away from the person. (Apparently, heat dissipates fairly well through the kind of shirts people wear in hot weather.) So, putting this particular device in a shoe would not cool down the foot because shoes don't dissipate heat well.

What would cool down the foot would be a device consisting of 2 parts connected by a hose, which would carry liquid from the part in the shoe to the other part (which could be strapped to the bottom of the leg). The liquid would carry heat away from the part in the shoe. A second hose would be needed to return the liquid to the part in the shoe. Call the part outside the shoe the radiator.