Why not use 2 thermistors. One would be of known type and characteristics. The other would be the thermistor under test. You could have a couple of baths set up in styrofoam cups. Put each pair of thermistors in the cup, let them stabilize and then take measurements. I'd think that after 3 or 4 different temperature readings, you should have a reasonable idea of what the curve should look like. The wider the gap from least to greatest, the better, of course. Mainly, I'm thinking that you could compare the unknown thermistor to different thermistor charts to determine which one you have. I know this isn't the automated test you would like to have, but at least you would have something to run with.
If you were to plot several thermistor curves in a spreadsheet and then plot the points you measure from your unknown thermistor, you could do a visual curve fit and a little SWAG to determine the thermistor.