High Precision Temperature reading, over a small range
I would use a platinum RTD for this purpose. Some precision thermistors might also be suitable. 

If you calibrate the sensors and signal chain individually at the triple point of water (single point calibration) then the accuracy of the sensor should be fairly good over such a narrow range. 

The optimal current will depend on whether the sensor is in contact with the water and on sensor construction (self heating variation) but at say 0.2mA a 100 ohm RTD will give you a fairly healthy 77 uV per millikelvin, so a good performance signal chain should not be limiting.