If I understand what you're trying to do, I think you may be able to run the experiment backwards to more easily figure it out. I'd recommend focusing on junction to case characteristics first - the case to ambient will have a lot of variables.

With the case attached to an "infinite" heat sink near ambient, or even regulated separately, or at least monitored, and the thermal regulation loop in action, you can watch what happens when the loop is disabled and the heating power is shut off. The thermal time constant should become evident. I believe it should be mostly a single pole, linear response.

You can set up a normal external circuit to run the device, but add provisions to override the loop and utilize Q2 for temperature sensing on demand, then digitize the thermal response curve.

If better accuracy is needed, you can use the old trick of measuring Q2 at two different collector currents, say in at least an eight to one ratio - an old-school current DAC is easily set up for this task, and can be directly digitally driven and synchronized with the measurements. The cycle/sample rate would have to be much faster than the expected thermal bandwidth, and the average power dissipation of Q2 due to measurement current would need to be included in the analysis.

This whole process - let loop stabilize, switch to measurement mode, switch to normal mode - could be repeated indefinitely, and the results averaged to get more precision.

Ed

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