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.

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