This appears to be a software bug in macOS or AMD's drivers. Plugging in an external monitor at certain resolutions (1440p@60Hz in my case) will cause the AMD GPU to draw 18-20W constantly, no matter what it's doing. This causes the total system draw to increase from ~10W to ~30W. All that heat has to go somewhere. If I change the resolution of my external monitor to 1080p the AMD GPU drops to ~4W and the fans are quiet again. A lot more information available in this long MacRumors thread:
https://forums.macrumors.com/threads/16-is-hot-noisy-with-an...