Is Accuphase E-560 a good match for Thiel CS 3.7?

Great amp, great speaker, bad match IMHO, that is just not the right amount of power for the 3.7, as Mmike84 says, I would think you need 100w minimum, and if you want Class A, that is going to cost $$$$.

Yes, it is not that the E-560 won't sound very good with the Thiels, it will and as a Class A amp it will sound like more watts than a similar Class A/B wattage rating, this is certainly true with the Pass Class A gear, but it is not an endgame amp with the Thiels, you will from time to time hear the limitations of the low power rating, especially with complex music with strong dynamic swings. It will sound wonderful most of the time, but not all of the time, through no fault of the amp's quality, but the Theils really don't come into their own with out more power and current capability, so if you want the best from your Thiels, I think you have to find another similarly fine amp, but with the power the Thiels demand to perform their best. Do note that Theil recommends a minimum of 100 watts and up, if you could get away with 30 watts, they would love to tell you that as it increases the number of suitable amps, but I would take them at their word, they know their speaker (very well).