The Pi Foundation just announced the second iteration of the compute module, usefully called the Compute Module 3. In their press release they've dropped some fairly hand-wavey statements about the module's current draw and subsequent thermal properties:
With a few caveats, the CM3 can be used a drop-in replacement for the CM1 since they are pin compatible; the CM3 is 1mm taller, however, while the CPU can pull a lot more current from the VBAT power supply line and will generate far more heat under heavy load.
All the fun applications for these things I can think of put them in pretty tight enclosures, which isn't ideal for high temperatures. How much current does a Compute Module 3 draw during heavy load, and what temperature does it reach at that point?