Voltage/temperature in steel wire
I think the only problem is to find the resistance-temperature dependency of the wire.

I wouldn't rely on published coefficients or tables unless you are very sure they refer to exactly the same steel alloy of your wire (I can imagine that you don't know it exactly).

I'd measure the resistance-temperature relationship by myself as follows (see picture):

Build a device using a hot air gun to create an air stream (red) of known temperature.
You can measure the temperature of the air stream by a conventional electrical sensor.
The temperature of the air can be controlled by the power feed to the hot air gun.
You probably have to take some care that the air is mixed enough after heating so temperature is homogeneous.

Use the air to heat a sample of the same type of wire (brown; maybe of larger length to get a more accurate result) and measure the resistance of that wire in the interesting temperature range.
Of course the resistance of the leads connected to the sample wire must be negligible  (e.g. by using thick copper wire) and the connection must be heat resistant at the interesting temperatures and resistant against oxidizing; at least for short time. I.e. you can't use soldering; I suggest crimping or welding.



Once you have determined the resistance at several different temperatures in the interesting range you can fit coefficients of an appropriate model function (the most simple model would be a linear regression with only two parameters: slope and intercept) and use it backwards (inverse function) to determine the temperature when resistance is given (measured).