A hot wire thermometer seems simple, but I have found them be somewhat complex in real situations. Simultaniously using the wire both as a heater and thermometer is more complex. Lets start with some verbal experiments. The resistance of a wire is determined by a well known equation:

Rfinal=Rstart(1+alpha*deltaT)

This works well and is nearly corrrect for many metals. Platinum thermometers are good examples. The assumptions are that the wire is in a uniform temperature controlled device and that there are no temperature gradients along the wire. i.e. The temperature is uniform and thus the temeprature coeficient alpha can be used to calcualte any new temperatures of the ideal wire thermometer.

Real wires need to be mounted at each end. This creates a thermal loss from the wire to the mount, and the wire's resistance behavior can no longer can be quite described by the equation above. since the temperature is no longer uniform. The apparent alpha of the wire is normally lowered by the thermal loss at the mounts. The magnitaude of change of alpha is determined by the geometry and thermal details of the system.

A good way to play with this is to make a model of a wire consisting of say 100 small segments. Assign a temperature gradient along the wire. Compute the total resistance of the segments and then compute the apparent temperature from the resistance sum. The wire has a thermal gradient imposed, but you only get one total resistance (temeprature) from the calulation or measuermenrt

In the example above, you can also try changing the temperature of a single segment (dT=200 degrees) and see how much the total resistance changes. Finding hot spots in the wire is difficult. with just single measurement.

JDK