The LM185, unlike the LM185-xx parts, is a 3-terminal, adjustable voltage device. The LM185-xx parts are fixed-voltage,
2-terminal versions of the same part. For your temperature range, the LM385 commercial version suffices.One might consider increasing Fred's feel-good resistor to take more of the 28V supply dissipation--120R only drops 1.2V.
Lastly, have you measured your noise diode's output power vs. drive current? You might only need the resistor, and that would be simpler now, wouldn't it?
Cheers, James