If you know what temperature you want the rod to be, you can determine what its resistance must be based on its physical dimensions and the known resistivity of the metal it is made of. Thus you know what current must pass through the rod to obtain a certain voltage drop across the points were the current is applied for a given temperature.
I'm thinking of passing a current through the rod and using the voltage drop across the rod to control the amount of current so that the voltage drop remains constant, in a simple feedback loop.
The problem is, as was stated, a battery is not going to last very long when used to heat that metal rod. So, there is no point in determining what the resolution/gain of the instrumentation amplifier has to be for only a 2 degree change in temperature for a given metal.
If the current source can be separated from the control circuit and is controllable, then maybe that will work because the battery need only supply the control circuit.