WARNING : the "waveform" in plot 8 is exagerated -- it's actually only a 10% ripple.
Even a square-wave will give a non-exponential waveform. (I'm doing curve-fitting with about 10 parameters -- give me a curve and I'll fit it for you!!!) To make any real conclusions I'd need to see -- from the dummy run -- a) The temperature rise with full power, from cold, until stable, and then falling again. b) A run with full power at a duty cycle of 35% (Suggested by Cude) Given those, I could make a first-order guess at the eCat's power profile.