The character of thermal distorsion
As far as I can see, there is no doubt that thermal distorsion (or memory distorsion) exists in the theory, so the question is if it matters in practice. I have been thinking a bit more about this, and it seems useful to try to understand this phenomenon better from the theoretical side so we do not accidentally ascribe any non-existing mysterious properties to it.
I think we agree that the major thermal distorsion mechanism seems to be that the power dissipation of the transistor modulates the die temperature, which in turn affects the transfer function. We can model this temperature effect either as a voltage source in series with the base or as a current source in parallel with the transistor between collector and emitter. Temperature variations can probably be assumed fairly small and there is hardly any point bothering about the distorsion of the distorsion, so a linear approximation of the temperature effect on the transfer function seems sufficient. Also the relationship between power and die temperature can be considered linear, but we also have to take the thermal impedances into account, as peufeu describes.
So what we end up is a BJT where we have an extra voltage source in series with the base (or current source from C to E), the voltage of this source being proportional to the power dissipation. Lets forget the termal impedance for a moment. The AC component of the power dissipation will be of the form p = A*ic + B*ic^2, where ic is the AC component of the collector current. The temperature and thus also the distorsion voltage will be of the same form, which means it will essentially consist of a fundamental and a second harmonic. That is, we get 2nd order distorsion. Instead consider a cascoded transistor. Now the power and thus also the distorsion voltage will be on the form A*ic, that is we only have a fundamental and no harmonics! So in theory, we would not have any thermal distorsion in the cascoded case, since the thermal effect would only affect the gain. However, we have so far neglected the thermal impedances. This means the distorsion voltage is affected by some RLC network, corresponding to the thermal model of the device. But an RLC network does not introduce any distorsion (at least for us who think of distorsion as nonlinearities). The only thing it can do is to change the amplitude and phase depending on the frequency (some people seem to think of that as distorsion too). It seems thus that a reasonable approximation is that we get a distorsion signal which consists of a possibly phase shifted fundamental and second harmonic, and in the case of a cascoded transistor we only get a possibly phase shifted fundamental. Assuming this thermal distorsion is already much lower in amplitude than the signal itself there is no need to care about better modelling of the distorsion itself.
Hence, my conclusion is that although thermal distorsion is a different mechanism from the usual purely electrical distorsions, it will behave in the same way and be undistinguishable from ordinary THD.
Does anybody agree with me or does anyone spot any error in the reasoning?