A designer would take all the time to do all that. I don't design.....I play.

I would just throw the parts together.........measure ambient temp.........at two or three points. Compare with the timer counts.......determine a slope.......Now I have a counter count, this is proportional to temp.....and then display or use temp info for whatever is needed. Calibration is done with software.

You don't want to do this if other people are watching. Some suffer physically.

At best I might need to change a cap value or counter interval. It's quick and easy........but not professional. And someone un-familiar probably would be perplexed.

Once you understand what the controller is doing......some software techniques can make up for a lot of hardware slop.

I'm speaking hobby wise now.........not for school or to make a living.

 

You can buy small film capacitors with a 1% capacitance tolerance.

Alternately you could switch in an accurate resistor to calibrate the RC time constant.
That takes the capacitor accuracy out of the measurement accuracy, allowing the accurate determination of the thermistor resistance.
If you did that before each measurement it has the additional advantage of cancelling any temperature coefficient of the capacitor.