Why are my mosfet fuses blowing?

A short in the speaker should be audible at moderate levels; one or more of the drivers would not be working. It is also an unlikely scenario. Failures in speakers are typically something burning up because they were over driven. This results in an open, not a short. It is possible that something is physically touching inside that causes a short but you should be able to put your ear up to each driver and see if it is working.

The other simple test, assuming you have access to another set of speakers, is seeing if it blow fuses on another set.

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I like Herman's call. Try other speakers.

I'll bet it still gets warm.
Re bias makes sense as do output devices breaking down under heat / stress.

The temp of the output devices is much hotter than the heatsink and all it would take would be some bad / devitrified heatsink compound to really cook some transistors.

Also, please check out this link to the CS2.3 Thiel. This is the measurement panel from the Stereophile test.
IF this is your speaker, I wouldn't use a bridged amp for any reason. It is a demanding load with a pretty beefy low impedance dip and a pretty nasty hi phase angle, to boot.

http://www.stereophile.com/floorloudspeakers/220/index7.html

A short somewhere shouldn't be something that comes and goes. You only blow when you listen at high volume, correct? If it were a short somewhere, it should blow at any volume level. I would check with Thiel. The impedance of many larger speakers systems varies with the amount of power being put into them. I used to own a pair of Infinity Kappa 9 speakers- large, complex load. Although they were "rated" at 8 ohms, when I ran into the identical problem you are faced with- I kept blowing fuses on an Aragon and Audio Research amp- I made a few inquiries, and found that the actual resistance on the Kappa 9's could drop below 1 ohm at full load. That means you need a ton of current to drive it, and if you don't have that, you'll blow fuses left and right. If that's not the problem, check the amp bias. Checking and paying to have the amp rebiased won't fix anything if the problem is the speaker load. I got around this for a while by bi-amping the Kappas, but it was still a problem. Eventually, I got rid of the speakers. Alternatively, if you love them, you could try a current monster amp like a big Krell and see if that solves your issues...but that's a pricey fix. Good luck.

Thank you all for the great input. The speakers sound excellent (until the fuses blow) so it may be a power issue. I do have another set of speakers (Tannoy Monitors)which I can try to see if the amp still gets hot. P.S. Thanks for the link to the Stereophile article!

I'll bet the Tannoys do fine- no fuse blowing. Your issue sounds remarkably similar to mine. If that's truly the case, you could, if the Thiels allow it, bi-amp or bi-wire the system with a second Classe amplifier. Be forewarned, though, you still may very well run into problems. You might be better off selling the one Classe you have and looking for something with a ton of current reserve to push the Thiels- Krell, Levinson or Rowland come to mind. Krells can drive a locomotive. But make sure you've diagnosed the problem before randomly starting to swap out equipment. Finally, is the Classe a Class A amp? Forgive me for asking a stupid question, but I'm not overly familiar with Classe products. If so, it's gonna get hot no matter what kind of load it's driving. Whether is blows a fuse or not should be the key with the Tannoys. Don't just look for power- look for an amp with high current reserve. You can get a high power amp- my Aragon was 400 wpc into 4 ohms and it couldn't drive the Kappas- with not a lot of current reserve that will run into the exact same problem.