How to calculate resistance to use along with NTC 103 thermistor to measure temperatures between 0-100 degrees celcius
Thermistors are harder to use than the LM35- they are usually very nonlinear. 

You need the parameters for the model of thermistor you have, either the \$\beta\$ (and the associated \$T_0\$) or the Steinhart–Hart equation parameters. 

Once you have that, you can estimate the temperature as a function of the resistance. For example, the simplified equation:  

\$\frac{1}{T} = \frac{1}{T_0} + \frac{1}{\beta}\ln \left(\frac{R}{R_0}\right)\$

One common set of parameters for 10K thermistors is 25/85 3977. 

Of course you find the resistance from the ADC reading and a series resistance set up as a voltage divider. You would typically want to maximize the resolution near the temperature where it will be most used, so the series resistor can be chosen to be the same as the thermistor resistance at that temperature. For example, if the thermistor is ~5K at 43°C (and that is near where it will be used) you can use a series 4K99 resistor, and the voltage will be Vin/Vref = R/(R+4K99)  

Rx = \$ \frac{4990}{\frac{Vref}{Vin}-1)}\$

You would also want to move to a higher resistance thermistor and series resistor if the self-heating is excessive for your application.  

Rather than use transcendental functions of the S-H equation in your MCU you can do the calculations once and use a lookup table to do the conversion from ADC reading to temperature.