Here is a paper in the Review of Scientific Instruments on noise characteristics of thermistors. The abstract asserts finding a noise level of 2.7 uK RMS in the 0.01 to 1 Hz band. I don't have a subscription but I would bet 10 uK is doable using their techniques. Warning, you need to understand synchronous detection (ie lock-in amplifier) to get down to this level.

https://aip.scitation.org/doi/10.1063/1.4976029

Edit: This is the world you need to inhabit to get to the OP's level of measurement. There are excellent references after the abstract. Note, there is not much new here. These techniques go back over 40 years.

 

I think that without a calibrated very accurate voltmeter the measurement will have the doubt of error.
There are crystals with frequency drift per degree temperature listed on data sheet. It comes back to
calibration again. In this case it is a question of being able to access a good reference frequency signal.
I think the design of the Keithley 195A did a fairly accurate job. The Agilent 34410A 6-1/2 digit.

 

1) RE:""Have you considered what thermal noise will be at that frequency and 293°K?|""
I may allow to integrate if needed even 10 minutes long (however 1 minute would be less shameless).

2) Analog Ground - thanks a lot, I have institutional subscription. However, there are at least two international services giving complete, free of charge entrance for ANY ever published closed for pay scientific document on the Planet. How far I have explored, 99% of all common knowledge are based on those two sites help and would not be possible without of it.

 

2) Have you considered what thermal noise will be at that frequency and 293°K?

Beating 1/f and thermal noise is done with "Synchronous detection", typically using a "lock-in amplifier". It moves the frequency out to a low noise point of the pre-amp, away from 1/f noise, usually greater than 1 KHz. Then, the noise bandwidth is reduced to a fraction of a Hertz with a narrow bandpass filter. This is how to measure nanovolts.