Remove the inductor between the emitter of your transistor and the non-inverting input of your opamp.
More serious:
Your NPN transistor also adds a lot of amplification to your opamp, which already has 100dB or so of gain and that reduces stability margins and can easily lead to oscillations.
Your circuit is very much like a current source, and these are well known to need some extra tinkering to get stable. To give you plenty idea's of how to proceed, have a look at:
https://duckduckgo.com/?q=opamp+current+source+stability&t=hd&va=u&iax=images&ia=imagesI would also swap the thermistors and their load resistors.
GND is always dirty and you've just made a clean reference, so make use of that by placing your thermistors directly to your reference voltage. I don't know what ADC you use, but a lot of them do not like to measure signals close to GND
Also, if your whole system is radiometric, you do not have worry about your voltage reference. Why not simply take a LM317L, or a voltage regulator with 3V3 output? (and use 3V3 as reference).
Have you also considered self heating of your thermistors by their exitation currents?
If you only need to measure temperature once a second or so, then you can make use of that by disabling the power supply for them inbetween measurements. This can reduce the dutycycle (and therefore the self-heating) of the thermistors by a few orders of magnitude.