I figured you'd probably measured the draw with your lights, and since it's just a control signal, I assumed it wasn't a big draw and that they're probably going to be similar.
Like I said, it doesn't seem to get into heatsink territory until about an 800mA draw, with an ambient temp of about 35C. Handy site for those who want to verify such things:
http://www.ef-uk.net/data/heatsinking_JS.htm
Addendum: Even figuring a 200mA draw (100mA per channel), the 7810 doesn't seem to need a heatsink well into ambient temps that I'd call "inadvisable" in an enclosure. I'll more than likely be integrating a fan into the enclosure for some airflow, so if I ever approached the limit, it would probably be because the stand and enclosure were actually on fire.