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Silly question but how does a 4m aperture focused onto a smaller area not concentrate the heat and melt the instruments?

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It's highly filtered, you are only getting a small slice of all of the wavelengths. Only a tiny fraction of all that energy hits the photo collector. I believe the collector is also actively cooled, but I might be wrong there.

Yes, just 0.5nm of spectrum in the instrument used (https://dkist.virtualsolar.org/vanNoortfastcam/, see under “DataSetDescriptions.pdf”).

If the pixels really are 20x20km, located at 1AU, I get 500k photons (within that bandpass) per pixel per frame at 740 Hz, not counting optical losses.

Space solar instruments like HMI on SDO (https://science.nasa.gov/mission/sdo/) have one or more pre-filters in front of the instrument to block some light far from the passband and keep heating under control. I’m not sure if DKIST has such filters.

740hz is the frame rate you’re capturing at?

Not “me,” but yes, that’s the rate quoted in the document I linked about the instrument that captured the images in OP.

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