I'm really not convinced we're wiring this thing up correctly, also I'm very suspicious of plugging in an equation with assumed values of a, b, c and expecting it to work - do we really trust whoever gave you those values?
Have you tried measuring the resistance of the probe, using just an ordinary DC multimeter with nothing else connected?
Also, I'm not clear but I gather this thing has only two connections, and it is wired to a simple "mono" headphone-style plug with a screen/earth contact and a single tip contact?
Also, are you sure a 10K resistor is the right thing to use - are you sure there isn't any self-heating going on anywhere and a bigger resistor is preferred for this probe?
Without anything else connected, I think you need the following: a resistor conneted to +5V or +3.3V (doubt if it matters much); other end of the resistor connected to the "tip" contact; the "earth" contact wired to 0V. nothing else connected anywhere. With this connection, I would expect a voltage to be readable with a multimeter at the "tip" contact, somewhere nicely between 0 and +V, which might
vary very very slightly with temperature.
Chris's comments about calibrating it, maybe with a linear fit instead of the Steinway-Sausage thing
, is a good idea too, to get some rough readings. Theoretical equations are good in theory...