Thiel 2.3s are between 2 and 4 ohms between 100 and 1000 Hz. This makes for a real current demand on any SS amp. You should use be looking at amps with a power rating into 2ohms, and preferably a doubling of power into 8-4-2 ohms. They are reasonably efficient watts vs spl (>87dB/W/m) but lesser amps will suffer at higher volumes and just not sound as good overall. Thiel tells me they use Krell 600W monoblocks to drive their 2.3s.
I'm using what I think is the minimum, a McCormack DNA 0.5 deluxe (SMC rev C), in a moderately large (and acoustically dead) room and sometimes like to crank rock music up. The amp starts compressing at much over 100dB, with 106dB peaks. Granted, this isn't the ideal pairing for loud rock. My amp makes 120Wpc into 8ohms, 220 into 4 and 330 into 2, and is rated for 25A current. A more powerful amp would likely enhance the speaker performance at somewhat lower volumes too.
I'm also using a tubed preamp and generally 'cool' audioquest interconnects - this plus the dead room keeps the treble energy well in check. But as those above have already suggested, you simply can't skimp on the quantity and quality of power for these speakers. I would think you could do fine for $3K used.