Thermal Distortion your loudspeaker most likely suffers from it. But do you care?

Insignificant in properly designed loudspeakers. High efficiency helps keep distortion to a minimum.

Back when tubes were king, high efficiency speakers were very common because tube power was (and continues to be) expensive.

When solid state amps were commonplace, speaker efficiency started to go down.

The problem here is that it never helps to have an amplifier drive a speaker that is a difficult load and in particular low efficiency. The result will be higher distortion from the amplifier if nothing else, and that distortion usually manifests as higher ordered harmonics, to which the ear assigns the tonality of 'harsh and bright' and is keenly sensitive to their presence since it uses them to sense sound pressure.

So we've been hearing 'harsh and bright' for 50 years now. Some is the fault of amplifier design of course, but difficult to drive speakers don't help. 

So inefficient and low impedance speakers should be avoided if you want to get the most out of your amplifier dollar investment.

It's a question of balancing speakers and amplifiers.

If speakers are 86dB/2.83v/1m, then you better have at least 200wpc and preferably 400w good, clean undistorted power @ speaker minimum impedance.

Professional studios may have 1000wpc driving horn multiway speakers, usually without power eating passive XO.

Sadly, too many today have zero understanding of basic fundamentals and buy faceplates.

Modern high powered amps (400+ watts) that can run into a 1 ohm load can certainly burn pretty much any low impedance device up. How much heat is developed depends entirely on current flow which depends in part on the impedance of the load, lower impedance devices being more likely to heat up. How fast depends on the amount of heat sink is available for the device and how well it is ventilated. 

The most significant problem is not thermal distortion but failure of the device. Modern voice coils with Kapton formers are surprisingly tolerant. Although resistance does increase with temperature the effect is minimal. It might skew the frequency response of the speaker a little and decrease output or available power but it will not cause IM or Harmonic distortion. You can read about the effect here https://www.cirris.com/learning-center/general-testing/special-topics/177-temperature-coefficient-of-copper and here,  https://en.wikipedia.org/wiki/Power_compression#:~:text=In%20a%20loudspeaker%2C%20power%20compression,power%20of%20the%20audio%20amplifier.

Thermal compression can be a problem in large commercial concert systems. It is not a significant problem in home HiFi systems. It would best be characterized as inaudible. The sky is not falling and you need not go looking for 16 ohm loudspeakers. Take a deep breath and say,"OOOOOOOOHMMMMMMMM.... 

@atmasphere --

"Back when tubes were king, high efficiency speakers were very common because tube power was (and continues to be) expensive.

When solid state amps were commonplace, speaker efficiency started to go down.

The problem here is that it never helps to have an amplifier drive a speaker that is a difficult load and in particular low efficiency. The result will be higher distortion from the amplifier if nothing else, and that distortion usually manifests as higher ordered harmonics, to which the ear assigns the tonality of 'harsh and bright' and is keenly sensitive to their presence since it uses them to sense sound pressure.

So we've been hearing 'harsh and bright' for 50 years now. Some is the fault of amplifier design of course, but difficult to drive speakers don't help. 

So inefficient and low impedance speakers should be avoided if you want to get the most out of your amplifier dollar investment."

But what makes a speaker a difficult load also and not least involves the effects of passive cross-overs (unless this is implicit to what you're saying here, but it's unclear to me) in terms of their complexity and the (steep) phase angles presented, not to mention smearing of the signal here.

This is interesting due to observations I've made going from passive to active speaker designs (with the same speakers), where I've found going active with solid state amps makes for a sound more akin to the sonic imprinting of SET's; passive sounds more sluggish, heavier even and less resolved (but to some more pleasing this way), whereas active makes for a more transiently clean (less smeared), less grainy and more liquid and open presentation. Easier on the ears, and more fleshed out.

I'd have cherished the opportunity of using 16 ohm versions of the drivers used in my speakers (not least the compression driver, which is available in a 16 ohm version), having then both high efficiency, high impedance and passive filter-less speakers. I would assume though passive filters and their negation to be a similarly or even more important means of making the amp seeing into an easier load, certainly bypassing more complex passive filters. A "purer" low impedance load seems preferable to a higher ditto marred by steep phase angles, but I guess it also depends on the specific amp.