Hi Nathan,
lot of information missing.
What sort of temperature accuracy, stability, and resolution do you need. What is the physical arrangement of the wire, is it in an enclosure or free air. In an enclosure, the air can be heated to the working temperature, the air temperature is measured. If a radiant system in free air, then the object placed in the path can be measured. Issues like emissivity and thermal time constants all come into play.
Nichrome wire is most commonly used for heater elements, it is not solder-able, crimp joining is the easiest way to deal with it.
The simplest way to control it would be a potentiometer, in increasing complexity a bang-bang, PWM or PID controller if you need good stability. Electronic control will generally not work off 1-2V, so you are talking about a SMPS to get the voltage up to a level where electronics will function. Depending on the control method, it might still be more efficient than a potentiometer if you want to use a single cell battery.
You will find all of the information you need on the Web, look up "tables for nichrome wire in heating applications", it will allow you to take a first stab at the sort of wire gauge and current you will need for a given temperature.
Then depending on the sort of control you need over the temperature, you can select between passive and active systems.
If you need some means of calibrating/ monitoring the system, there are cheap digital temperature meters available that with calibration in a mix of crushed ice/water, and boiling water, should be good for a few degrees Celsius.
Without knowing a lot more, hard to add much, except to say that the physics involved in solving this is quite complex, so a mix of an empirical approach with simpler maths may be all you need, depends on your background, hope that helps.
After all of that, I used to build up frames for beehives, nichrome wire was stretched across the frames, a sheet of wax placed in the frame, and a battery connected briefly to the wire. It got just hot enough for the wax to melt onto the wire. No maths, physics, pots, or controllers. At the other end of the scale, I built up an experimental device, where a heater in an enclosure warmed small wood samples above 373K ,which used a thermocouple and a PID temperature controller, as I said, need to know just what it is you want to do,
cheers,
Richard
