1. Are You sure that diode excitation current is free from these oscillations?
2. Are You sure that diode is not demodulating some nearby WiFi/GSM signal / maybe neighbor just behind the wall?
3. Air conditioning influence or other temperature regulator ?
The diode current comes with a resistor from the 14 V reference to the ADC. So that should be pressy stable. The NTC also showed the same (or at least similar) frequency.
No air conditioning (it is winter anyway) and the heater system is way slower than 0.2 Hz to make any difference across the room.
The circuit is inside a mainly close metal box - though with an USB cable coming in and the PC using WLAN. Still I don't expect 0.2 Hz modulation from WLAN / GSM - that is usually faster. My initial suspect on low frequency oscillations was the DCDC converter as it uses some frequency modulation/ spread spectrum ( ~50 Hz range) that might hit a beat frequency with mains or the ADC integration time.
The effect reacts quite a bit to changes to the thermal (e.g. tilting). The other indication was the test with more voltage and thus heat at the regulator increasing the amplitude. So I have no doubt it is thermal.
The NTC side up, it still only a moderate tilt up. The actual regulator part of the heat source was still about the same hight overall. The temperature likely drifted up in that phase because the heat could spread out lateral better. Convection was for sure still active, just not oscillating. Even with the heat source side up, there is still air between the heat source and the top of the cause, so still room for convection, just with a different pattern. The overall temperature drops, as the warm air would not reach the other side that well.
Why it still oscillated with tilt in one direction and not with the other, I don't know - my vague expectation was more of the opposite. The point is not so much how it changed, but that is changed significantly with only a small tilt.
The convection can be stable, oscillating or with chaotic variations. The transitions are already hard to understand for a simple geomity like in the scientific papers.
The geometry with the PCB is too complicated to fully understand or model it. Fluid dynamics is already tricky with a simple geometry.
Especially in the chaotic case it only takes minute changes get quite different results. My system looks like is somethat oscillating, but not perfectly stable and possibly close to a chaotic range.