Copper wire hand heater
What you'll want to do is first figure out how much power you want to draw from your battery, all of this power will turn to heat one way or another.

Lets say you want 5W. Your battery is 3.7v nominal, so you need 5w/3.7v= 1.35A

To get 1.35A at 3.7v you need a resistance of: 3.7v/1.35A = 2.7 ohms

If your copper wire was 0.1ohm, the battery adds about 0.35 ohms, so you were drawing 3.7v/0.45r = 8.2A, which would produce 30W! perhaps more. That explains why your wire got so hot. And don't forget given the above assumptions 77% of that heat was being generated in the battery itself!

Ok so you need 2.7 ohms total:


If you use 22ga copper wire, you'll need a 145ft of it. Not
practical.
If you use copper wire + a resistor, say a 2 ohm resistor, then
almost all of the heat will be dissipated by the resistor, not the
copper wire. 0.1r/2.45r = 96% to be exact. This actually would be fine if   you get a nice power resistor like this one.
If you use 22ga nichrome wire, you'll need about 2.3 feet which is manageable. 


So now hopefully you can see why nichrome wire is used instead of copper. One additional advantage is that if you heat copper wire up so that it's very hot it will quicky corrode and break. Nichrome wire on the other hand will form a protective oxide layer and will not corrode.