It seems that one of the difficulties is imagining how something that is hot (a sunspot) can appear black. There is an example on Earth that I have personal experience with. It is called an optical pyrometer. It is a way of measuring the temperature of a body, such as the inside of a furnace. You have a device like a small telescope with an electrical wire / filament inside of it (like a lightbulb filament). You look at the object you want to measure and see the filament superimposed over it. You will see a red or orange background (if the furnace is hot) with a dark wire. You put current through the filament to heat it up. You adjust the current till the color of the filament matches the body and compare your calibration of current to temperature and read off the temperature. When the filament is cooler than background (but still hot) it appears black or dark.
There is a very nice slideshow explanation
here, scroll down to the slideshow link.