The LM399 datasheet specifies a temperature coefficient "\$\Delta\$T/\$\Delta\$Temp". The conditions state an ambient range but don't specify if that's with or without the heater on.
Which is it?
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If you read the Note 3: "These specifications apply for 30V applied to the temperature stabilizer and –55°C ≤ TA ≤ 125°C for the LM199; and 0°C ≤ TA ≤ 70°C for the LM399."
Means that the heater is ON and powered through 30V. If you use different heating power, precision might vary.