It does ! The effect is usually called 'power compression' and it can typically
knock up to 3dB off the speaker sensitivity with prolonged high power use. That'll
give you some inkling as to the temp rises involved.
Since such speakers are invariably used with 'active crossovers' on the inputs to
the amplifiers it doesn't cause any adverse issues with crossover responses.
The company that first made that 'red hot' claim was Precision Devices. You can
find a 1000W continuous rated speaker of theirs here.
http://www.precisiondevices.co.uk/showdetails.asp?id=17
Kapton voice coil formers are now the norm for decent quality speakers.
I have *never* seen a purely thermal failure in any *modern* voice coil.
Graham