This was super fun build, I did one years ago. Today I powered it up again after it have been laying on under a pile of trash above the workbench for several years.. After an hour warm up, both my Keithley 197A (LM399) and the 1N823+OP07 reference the value set to 9.9999V which is not bad, it still is "too good" for the best measuring equipment I have the 197A.
The current source I was using were simple.. Forementioned Keithley as current meter in series with some 10 turn potentiometer, powered with Thandar lab supply (or were I driving the PSU against current limiter and using it as current source... can't recal). Then my MeraTester v640 (100meg, 1.5mV FSD) as a null detector against another channel of close enough voltage from Ch2 from thandar supply. Then the heat was cycled first by pinching the dut (1n823), then adjusting the current in a point where no movement of null detector was seen.. After that I did use a 12V lightbulb wrapped to foiltape (to allow only heat) put under and contact to the DUT, then again adjusting the current to null out the voltage on null detector on this rather violent heatcycle.. This also involved to disassemple the current measuring setup and to use the Keithley 197A to measure the TC voltage after point was found. Repeated this to three 1N823s and did choose the best one (can't recall did I choose the one with widest TC region or something can't recal)..
Then calculated the needed resistance between the 1N823 and 10V output.
Calculated the needed resistance for amplification multiplier resistors.
Sorted out all my handfull of 15ppm 0.1% resistors for TC. This was done again with Thandar as supply and 4 of same value resistors as Weatstone bridge configuration. One as a dut and 3 others as voltage source for null meter. Dut temperature cycled with my fingers and variation detected with zeroed MeraTester v640 in lovest range possible (mostly 1.5mV). I might have used a 10 turn Bourns pot again at one leg of the bridge.. Can't remember all details, it was a mock up one weekend setup, with a few beers.
Calculated series parallel networks to match the needed resistor values and then
constructed the circuit in manhattan style to full copperclad board with attention for mechanical stresses.
As an afterthough I should have put more efford to the amplification multiplier resistor network it is sub optimal part.