Did the Persians take over Greece after they won Thermopylae?

No. The Persians won the Battle of Thermopylae, but this was a tactical victory, not a strategic one. While the delay inflicted by the Spartans and their allies at Thermopylae was significant, it didn't prevent the Persian advance into Greece. The Persians ultimately lost the Greco-Persian Wars. The victory at Thermopylae allowed the Persian army to proceed, but the war continued and the Greeks ultimately repelled the invasion.