Why can dark silk feel elegant and cool indoors but become hot fast in direct summer sun?

Answer: Sunlight absorption wins

Sunlight absorption wins ✓ — Correct. Indoors, your skin mainly notices contact heat exchange with the fabric surface. In direct sun, radiant energy becomes a much larger input, and dark colors generally absorb more of it. The same silk scarf can therefore feel cool in a bedroom and hot on a sunny sidewalk because the dominant heat pathway changed.

Smoothness blocks sunlight — Smoothness can make skin contact feel different, but it does not block incoming sunlight. Under direct sun, radiation reaches the cloth before your skin-touch judgment even begins. A smooth dark surface can still heat quickly if it absorbs much of that radiation.

Only air temperature matters — Air temperature matters, but direct sunlight adds a separate heat input. Two pieces of clothing in the same air can heat differently if one absorbs much more radiation. The useful distinction is between contact coolness, which starts at the skin, and solar heating, which starts with light hitting the fabric.