If you look at the phase angle/impedance curve TLSGuy just posted, and if your MKII has similar characteristics, you can do a quick experiment by setting the crossover to 150 Hz or even 125 Hz. You should be able to see the temperature all else being the same (such as the same volume, playing the same music) drop somewhat. Not a solution but just an experiments.
Again a good solution is to grab a Hypex amp, they are cheap in NA but may cost a little more in Europe.
VTV AMPLIFIER Stereo Hypex NC502MP NCore Amplifier 500WX2 | VTV Amplifier
VTV AMPLIFIER Stereo Hypex NC502MP NCore Amplifier 500WX2 | VTV Amplifier
Buchardt also sells Hypex amps, but only integrated amps unfortunately.
The easiest "fix" is to back off your volume setting by 3 dB, that's to turn it down 6 clicks. If you are willing to that, your amp will run cooler for sure and the risk of damage overtime will be much reduced. If you turn it down even a little lower, and use the 8 ohm setting, you should notice improvement in sound quality.
That brings up the following questions:
1) What is your volume setting typically speaking?
2) Do you always have Audyssey on?
4) Do you always have Dynamic EQ on.
5) What is your crossover setting?