Verification on Ohm's Law?
Hmm, I think, you mixed up several things.

First, your wiki page states that Gauge 22 has about 1 Ohm/ft, so the thicker gauge 20 should have about 0.6 Ohm/ft. 

Next, the last table from wiki states that resistance increases by up to about 10% when heating the wire to 2000°F, so I have no clue why your resistance changes so much, and why it decreases. 

Also, you seem to correlate the temperature to the current, because the wiki page does so. But note: That temperatures given on wiki are temperatures for a straight, horizontal NiCr wire in resting air. That is, the temperature is the result of an (almost) constant heat production of the wire and the (temperature dependent) heat dissipation by convection in air. If you plan to wrap the wire around your grips, heat will be transferred to the grips, and the wire will not get that hot.



Now, for your case, the resistance of the NiCr wire is always the same for the desired temperature range, about 0.6 Ohm/ft. So, a single 10ft long wire will have about 6.0 Ohm. 

At a constant voltage from your motorcycle of 12.7V, you'll get about 2A through a 10 ft wire, which gives about 25W. If you need less power, try a longer cable: 20 ft has twice the resistance, you'll get about 1A and so, 12.7W.



Now you write that you want to regulate the power of your heater. The problem is that the potentiometer has to take lots of power. Let's say you have your 10ft, 6Ohm wire and a poti set to 6Ohm. (This is like having a 20ft wire, just one half replaced by the pot) The entire setup generates 12.7W of heat, but just half of it is generated by the wire, the other half is generated inside the pot. A potentiometer for more than 6W is... large.

Due to your skills, I would recommend something like this:







simulate this circuit &ndash; Schematic created using CircuitLab

Depending on the state of the switch, current flows through either one or both 10ft wires, which results in a heating power of about 25W or about 12.7W. Using a switch with more states, you can get finer power settings. (Also, you want to switch the heater on/off, right?)



Back to the table with the temperatures: I wrote that the wire doesn't become as hot as written in the table, because it dissipates the heat to the grip. But if it's not in good thermal contact with the grip (e.g. at the terminal where it connects to copper wires), it still will become hot at those spots. I'd recommend to use a thicker, but longer cable, because then you have less heating power per length, and those spots would not get that hot.

Finally, use a fuse rated for about twice the maximum expected current. because if something goes wrong and you get a short circuit between the windings of your wire (or to the metal of the steering rod), it can still become very very hot and cause a fire.