To be clear, a poor weld joint particularly with the sandwich type of joint can indeed produce microvolts of noise and offset, PTF resistors utilize sandwich welds. Further more, there are no end caps on precision resistors they cause way too high TCR, those are almost always relegated to power resistors. With a sandwich weld, it can initially appear good but deteriorate with time and heat, while 40°C isn't particularly hot it is certainly hotter than room temperature. I have seem many a sandwich weld joint pass all kinds of testing including high temperature stress and still fail later on, on the other hand there are sandwich joints which can pass all testing and remain good for the rest of the component's life.
It was said earlier that the circuitry was in an 40°C oven so unless his oven is fluctuating, temperature is not the primary suspect, although he did not mention how long he had been running the circuit in the oven. As I mentioned the diode's quality could also be suspect for unexpected noise.