There is no really sharp change in the style of architecture between the Archaic and the Classical periods. One blends gradually into the other. For no particular reason, we actually have more archaic temples that survive than we do classical temples. The most famous surviving classical temple is the Parthenon in Athens, which mixes the Doric and the new Ionic styles.
The Athenians built the Parthenon, a temple to Athena Parthenos, or Athena the Pure, in the 440s BC, using money from the Delian League’s treasury. It replaced an earlier temple that the Persians had burned. The Athenians wanted the Parthenon to be the best temple ever built, and so it was made entirely out of marble (even the roof-tiles!), and with eight columns across the front instead of six, and with carved sculptures on the metopes. To make the Parthenon look even more like it was reaching for the sky, the architects curved many of its lines upwards in the middle.
Also in the Classical period, the Greeks began to build permanent stone theaters, like the Theater of Dionysos on the side of the Acropolis in Athens (right under the Parthenon). The first Greek theaters were just people sitting on the hillside so they could see the show, but now they built stone seats into the hillside so it wouldn’t be muddy.
Make This Model Greek Temple (Usborne Cut-Out Models Series), by Iain Ashman (1998)
An Ancient Greek Temple, by John Malam, Mark Bergin (2001)
Greek Art and Archaeology (3rd Edition), by John G. Pedley (2002). A lot of good information and is pretty readable. Plus, the author is really an expert in this field.
The Archaeology of Greece: An Introduction, by William R. Biers (1996). Biers writes very clearly and has a lot of good pictures.