The fuse temperature depends on the average current over a period of 100 ms or more. It does not track the signal waveform. If it did, slow-blow fuses for AC couldn't exist.
I wasn't thinking of it tracking the instantaneous signal level. I agree it's a thermal issue with long time constant, sorry I did not make that clear. It does track the average power and that varies with listening level and so forth.
From previous posts, the temperature of a fuse remains fairly constant once warmed up. Voltage drop does not cause modulation and does not cause distortion. That is an incorrect assertion. I whole heartedly agree that putting a fuse in line with a speaker is poor design.
No, voltage drop that varies with signal causes distortion; it creates a nonlinear result. The modulation will be different at different power levels; the temperature is only constant for a given steady-state power (current) level so changing power (SPL) changes temperature and thus voltage drop.
The distortion a speaker fuse adds usually shows up in power sweeps on the bench. And generally only when the fuse is near its breaking point when the resistance rises rapidly. As far as audibility is concerned, it is in the mud, and like many other things audio, the marketing that played up lack of fuses in the output signal path neglected both its impact and the orders-of-magnitude greater distortion generated by the speakers themselves. But, back in the 1980's or so when vanishingly low amplifier distortion numbers were all the rage, fuses were eased out of the signal path because they added measurable distortion. Extremely high damping factors (or low output impedance, same thing) were also in vogue and again a speaker fuse increased output impedance so was undesirable (some amps put feedback after the fuse and/or moved the fuse elsewhere in the circuit; eventually different protection schemes were implemented).
I don't think any of this matters for audio, at least as far as the end user is concerned. I have had to deal with metal tempco and such designing precision ADCs and DACs, where temperature change caused the metal resistance to vary, and upset my fine-tuned trimming algorithm since metal and resistors varied differently (so a precision-trimmed resistor did not track others over temperature due to the metal connecting them). Made for a layout nightmare. That was on an IC, however, and at the end was fixed on the chip so the customer never saw it. There was much gnashing of teeth and hair-pulling before I solved it, however. And again there it was a long-time thing. The really nasty thermal settlers are the ones inside the transistors themselves...