Electrical resistance converted to wire temperature
The resistance of the wire will be 12/10 = 1.2 ohms

R = rho * length / Area (where rho is the resistivity of the material chosen, remembering to convert length etc. to appropriate unit)

then Area = rho * length /1.2  this will give you the cross sectional area. 
 Look up the X sectional area to give a wire gauge.

All this will do is give you a wire of the correct length and resistance for a given material.

The temperature the wire will 'get up to' depends on how quickly energy is lost to the environment. (Power out = power in @ equilibrium temperature). 

There is no set formula for the final temperature of the wire because there are so many variables e.g. how well insulated the wire is, how it is wound (large or small coils), in air or vacuum and so on and so on ...

You have two basic options.

Experiment: Get your wire (as calculated above), feed it with 12V and see what happens temperature wise.

or

Devise a circuit to limit how hot the wire gets (within your desired range) by controlling the amount of power dissipated in the wire. (e.g. - fit a thermostat)