These are actually the roots of the trees, not the trees themselves. The temple was built in the 12th century and was abandoned in the 1400s. It wasn't until the 19th century that it was "discovered" by archeologists.
I would recommend you come to the Blue Lagoon directly from the airport if your flight arrives at 7,8,9 in the morning. Hotel Check-in is not until 3pm and this place will relax your mind a body from the over night flight.