Since JWST is trying to pick up weak infrared signal from the furthest reaches of the cosmos, any amount of noise would distort our measurements.
The telescope itself will naturally radiate infrared heat (much like our own bodies do), which is exactly what the instrument is trying to measure. This is why they're cooling the instrumentation side to such a cold temperature that it won't emit infrared energy and ruin the science.
Allright, so is that why it takes ~6 months of waiting time now? Would it not be possible to just measure the heat radiated from JWST and subtract it from readings?
Measure thermal noise? The amount of information contained in the black body radiation of a warm (well, really cold, but not cold enough) object must be absolutely immense, at least when you care about a signal at the level of single photons. Trying to capture it with sensors is futile. Sure you can try to do some noise suppression with a simplified model/probability distribution, but that won't work well if your signal to noise ratio is 0.00001.
That would be like throwing a beam of a light from a powerful flashlight 10 cm away from his face when he watches night scenes from last season of Game of Thrones, and saying ”just ignore these 1000 lumens, tell me what is happening?”
The telescope itself will naturally radiate infrared heat (much like our own bodies do), which is exactly what the instrument is trying to measure. This is why they're cooling the instrumentation side to such a cold temperature that it won't emit infrared energy and ruin the science.