The "maximum power rating" is only relevant for you, if you decide to use the NTC for fluid detection or similar, means when you use a heated NTC.

But in your application, precision measurement at +37°C, only a non heated NTC can be used. The "dissipation constant" of 1mW/°C tells you the maximum power that is allowed to be dissipated in your NTC to provide +-0.1°C tolerance, which is 100µW.

At +37°C your 10kOhm-NTC shows a resistance of about 6kOhm (assuming a Beta = 3890K). So, no more than U = SQR (100µW x 6kOhm) = 0.77V must drop across it.

Would you want to measure up to +50°C, then the maximum voltage drop should be less than U = SQR (100µW x 3.6kOhm) = 0.6V.

Normally, you build a voltage divider consisting of NTC and precision resistor (as you already plan to do), which shows equal resistances at the center temperature of your measurement. So, you should choose a 6.2kOhm metal film resistor. This arrangement shows highest sensitivity, means yields highest voltage change per temperature change.

Sometimes, the NTC resistor is paralleled by a precision resistor to somewhat linearize the rather unlinear R/T-relationship of NTC. But for your precision measurement the result of this paralleling is not good enough. So, I would use a look-up table to compensate for the unlinearity in combination with a ratiometric measurement to first order eliminate fluctuations of Vcc, means make Vcc be your reference voltage of ADC.

Unfortunately, your 10kOhm-NTC is too low ohmic to work at Vcc=5V. I would choose a 100kOhm variant. So, a 100kOhm-NTC in combination with 62kOhm metal film resistor at Vcc=5V would be a suited combination.

Kai