It's possible with the right components. Both AMD and Intel have CPUs that are designed to be energy efficient and run cool. Entry/budget GFX cards are sometimes passively cooled out of the box. As long as you put a good 3rd party cooler on the CPU, it should manage. But, I would always advice to a least put some fans in the case to create airflow around the parts. A completely passive cooling solution will have a lot of heat build up inside the case.
IMO it's doable for a purely media-centered PC (HTPC), doing nothing more than playback audio and video. Intense usage of the CPU or GPU, for example encoding/decoding and gaming, put out a lot more heat than streaming media.
You might also want to use external storage in such a case. The more heat-producing components outside the case, the better.
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