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....