How do electric ski boot warmers work?
 

I bought a set at a garage sale for $1, and one has a broken plug. If I can
figure out how they work, maybe I can fix it.

The cable that goes into the boot has 8 wires; they are soldered together in
three groups of 3-3-2. The power supply has three prongs. It also has a
dial with 5 settings. I tested the voltage on the power supply. One
setting is off, and the other four have 2.7v between prongs 1-3 and 2-3 and
0v between 1-2. So the neither the voltage nor the contacts change with the
setting. (The power supply is marked 2.4v)

So, how do you think this works?
What changes when you change the dial setting?
What is the difference between prong 1 and prong 2?
Is it reasonable to assume that 3 wires each go to prongs 1 and 2, and the
other 2 wires go to prong 3?

I did contact the manufacturer and they said they don't support old junk.

How do electric ski boot warmers work?
 

According to Toller :
I bought a set at a garage sale for $1, and one has a broken plug. If I can
figure out how they work, maybe I can fix it.

The cable that goes into the boot has 8 wires; they are soldered together in
three groups of 3-3-2. The power supply has three prongs. It also has a
dial with 5 settings. I tested the voltage on the power supply. One
setting is off, and the other four have 2.7v between prongs 1-3 and 2-3 and
0v between 1-2. So the neither the voltage nor the contacts change with the
setting. (The power supply is marked 2.4v)

So, how do you think this works?

Sounds like there's multiple heating loops. The amount of heat
generated is determined by how many of the loops are activated and
how much current is driven thru them.

The switch may be switching between resistors (or even phase modulation)
to control how much current goes thru each loop.

Try measuring resistance on the wires going into the boot, and see
which ones are attached together. Then, rig the control box to
feed a "common set" of wire loop. Eg: one end on pin 1, the other end
on pins 3, and see what the voltage does when you switch it.

If it's modulated, it gets tricky ;-)

In one older system I saw (old Lange racing boots), there was a battery
pack inside the boot sole which is charged by a wallwart (obviously
not on the hill ;-). The heating elements were either full on or off.
--
Chris Lewis,

Age and Treachery will Triumph over Youth and Skill
It's not just anyone who gets a Starship Cruiser class named after them.