Electriconically controlled variable resistor
You made something simple look complicated. You need to feed the resistor through a current generator. There are many schematics available on the net. I suppose you want to have a ground point to measure voltage on the wire then compute the temperature from it. 

Which solution you use is highly dependent on wire resistance and current needed. 

For small wire voltages you can use a simple resistor, For V1 >> Output voltage and R1 >> R_wire the circuit is a very good approximation of a current generator, for wire resistance between 0 and 0.2ohm the I error is in the range of 0.2%







simulate this circuit &ndash; Schematic created using CircuitLab

If the wire has a higher resistance or you need a higher voltage you can adjust R1 to obtain the voltage or current you need. The error would be given by (delta R wire across temperature range)/R1. 

If the wire resistance is higher and you need voltages that are not much less lower than the power supply voltage then use a current generator like this one or search google for current generator.