Measuring transient thermal impedance
You can see in your graphs that, on a time scale of about 50ms, your Hfe doesn't change much more than 3-4%.  In your first schematic, however, Vbe is your parameter which will contribute more to the distortion, and that's under 2% variation.  These represent the maximum slopes of those curves, starting at t0.

50ms is a complete cycle at 20Hz, typically the lowest frequency of interest in audio design...so there will be very little distortion from an audio standpoint.  Over the longer term, the gain may change slightly, but this won't cause harmonic distortion.  If it did, the distortion that comes from your sub-$10000 speaker system will easily overwhelm it.

If you're a real perfectionist, drive the finals with an op amp and take the feedback from the output.