With a RC filter you have the OPs input current (bias and curent noise) and the Johnson noise of the resistor.
With a reasonable size capacitor (e.g. 10 µF) the upper frequency limit would be well below 10 Hz. So the relevant noise is not 0.1 to 10 Hz, more like 0.01 to 1 Hz or even lower. The main parts there are the 1/f noise of the LM399 (or similar) and the 1/f noise of the OP. Especially the current noise may have quite some 1/f part.
So the OP07 would not be a good choice for high resistance (e.g. > 30 K). More like OPA202 as a BJT based one with low current noise, or an AZ OP like LTC2057, AD8628 or maybe max4238. The specs for the current noise of AZ OPs seem to be not very relable - 1 would not count on all the numbers there, especially when very low. I would consider some 100 K a reasonable upper limit as than one starts to have to worry about leakage curents in the pA range that may change. The main noise source would still be the LM399, even if using 4 or so. Still filtering the reference is limited. The filter will also need quite some settling. It is not only the RC time constant, but there are also slow DA effects that need to settle when it comes to settling to something like 1 ppm of the final value. This part starts smaller but can be 100 or 1000 times slower.
The capacitor may also need a reasonable stable temperature (e.g. thermal shield): I can see a small thermal effect even with only some 5 K and 4.7 µF (MKS with 3 x muliplication), it would get more with higher resistance.
If it is about a more pulsed operation (e.g. 99 ms zener and 1 ms temperature measurement) the more suitable way would be a switch to turn off the connection when in temperature mode.