No thermistor in the world is linear, this is the only real downside, they do output a large signal though, this is why they are used, there is no amplification needed, generating with it the unwanted side effects of amplyfying everything such as noise, offsets, drifts etc, these are about the most un linear devices known to man.
The thermistor/temp sender is the same one as the air temp sender, just in different housings.
Using the pedal to keep it going will do no harm, but it does get a different signal as fuel is added due to tps reading, and more air flows as well.
Just check the co when hot, if this is ok, then you can try a slight tweak.
If wanted you can work out the resistance versus temperature with
R=Ro exp(Beta/T-Beta/To) formula, if interested.
tabetha