Hi

AD 590 is given for a +/- 0.5 °C precision ....

so, +/- 0.05°C do not mean aything here, also, do you really think you can make a current to voltage amplifier able to sense as small as 0.05 µA ...( 1µA/Deg )

so, it's simple : without special calibration +/- 0.5°C !!!
repetability is +/- 0.1°C : so do not try more than +/- 0.1°C, that with a fine calibration ...

Alain