With a resistor I get a stable reading, though the last one I tested as a direct 1:1 replacement was only 100 ppm/K grade - so a little slow drift, but not much.
I also saw corresponding variations with a diode in place of the NTC, and little variations with a low TC Zener. The NTC also shows a comparable signal with a lower current (10 µA and 30 µA instead of 100 µA used for most tests). So I have no doubt that it is really a temperature variation.
Changes from the outside (e.g. touch the case, light diretly on top) are visible too, but slow and with some delay. That is more 1 minute and longer and no easy way to get a 5-10 second periodic signal from the outside. It takes quite some warm up time to get the temperature stable enough to see the small variation directly and not have them burried in the drift.
A fast thermal effect may come via the air pressure, e.g. from wind gusts or closing of doors, but that is usually not that periodic and not much on a low wind day.
Unstable convection (as regulator oscillation or more chaotic) seens to be not that uncommon and not that easy to predict. The amplitude of the variations is still moderate, but when looking for very low noise in the LF region it can be an issue.
Chances are other ciruits, especially when running a bit hot could have similar temperature fluctuations.