How do you cool them? Dry ice?

Also how do the batteries hold up, or are you powering it off a cable then?

They have active Peltier coolers and you use mains power, a portable battery box, or the 12V output from your car. You also need to power a computer or laptop to capture the images.

Roboscopes like the Seestar are an all-in-one kit and have internal batteries that last about 3-4 hours (although for the moon you don't need more than a minute or so). The S50 can take uncompressed video, which you can then process as GP describes but, compared to a more powerful setup, the camera is 1920x1080 and uncooled, the framerate is limited to 30fps, and it only has a 50mm aperture.