I replaced the fuse in the box on top of the battery and the cooling fans worked and the a/c blew cold air. Then, the new fuse blew. Now what?

now start looking for a short, because something is drawing more power than it should be.

Get a multimeter and a copy of the bentley repair manual.
Hell, you might even have a DTC that just hasn't turned into a CEL yet.
Which would give you a better idea of where the short is.

So, get a vag-com cable, or go to autozone and have them scan your car.

Sounds like thermostat.

Can the thermostat cause the fuse to blow? (3 fuses under the cover on top of the battery, fuse on the left that's blowing)

Ah sayud, can the thermostat caws the fuse to blow?

Could it be one of the cooling fans that's the source of the short? Of the three fuses on top of the battery, it's one on the left that burns out.