Electrical – ny difference between the terminals of the rheostat

A CMOS chip ideally acts as you suggest with the dynamic power consumption proportional to the switching speed and the square of the power supply voltage (and the static power consumption with clock halted zero).

However, as you try to lower the supply voltage (for reasons obvious from the above) the transistors no longer quite turn off all the way, and an ever larger static consumption appears. This is called subthreshold power leakage and increases with temperature. There is also gate oxide leakage.

There are mitigation techniques, including circuit design and using exotic materials such as high-K dielectrics that can reduce the effect. At one time it was predicted that static power consumption could approach dynamic power consumption but I don't think that has happened.

It probably is feasible.

But: you need to realize that even for electricity, conservation of energy applies! So if you want to produce 10,000 Ws (wattseconds) = 10 kJ of heat, you need to have that much energy in your battery.

So, in your place, I'd start by calculating what amount of heat you want to produce. That's really easy. Calculate the amount of material (ie. flesh) you want to heat up, multiply that by the specific heat of the material (use the specific heat of water, flesh is mostly that stuff), and then you know how many Joule you need. One Joule is 1 W · 1 s.

Then divide that by the time (in seconds) you want to allow the heating to heat up that much material, and you've calculated the power (in Watt) necessary to heat up that amount of material that fast.

Now, I don't believe you know nothing. You've probably heard of 1 W = 1 A · 1 V. So if you have a 12 V battery, in order to produce 1 W, needs to make \$\frac1{12}\text{ A}\$ current flow. If you need 120 W, you'll need 10 A. It's that simple.

Now that you know how much current you need to spend, you can calculate two things:

1. how long your warmer should last with a single charge. Most batteries are rated in "Ampere hours", Ah, so take one battery that you think would be of acceptable weight and size, and figure out how long it will be able to source that current.
2. how much resistance your wire needs to have, because, Ohm's law, U = R · I -> R = U / I (the resistance is the ratio between voltage U=12V and the current I). Heater wire has a fixed resistance per length. You can thus calculate the length of wire necessary.

This doesn't address things like maximum power impedance matching etc, but it does in theory give you a good idea of what your system needs to look like.