I'm not sure why, but I've always thought it interesting that radiation scales as a fourth power. It's unusual to see forth power relationships in fundamental scientific processes.

Black body radiation scales with T^4, but you're relying on one particular band. I suspected it scaled, but T^4 seems rather unlikely ;-)

Most materials scale with T^4. You would need a very weird radiance spectrum to do anything different.

That said, we are talking about something that has a weird radiance spectrum as a selling point, so, expect some deviation from the standard T^4 curve.

I would assume it scales at K*T^4 where K is a constant < 1 and gets smaller as the band narrows.