Once you reach the "porch" of the green marble temple, find the only green torch. Press the use key on it to lower a lift on the opposite side of the porch. Ride it to the top, where a soul sphere is located.
After entering the temple, hug the left wall until you reach a security armor overlooking a bridge crossing some lava. The ground it rests on counts as a secret.
From secret 2, backtrack a bit and you'll come across a stairway that dips down in the middle, with an opening to an outdoor area at the lowest point. Open the green marble wall across from the opening to find an ammo cache.
Halfway through the long red tunnel in the beginning of the level, there will be a niche to your right. Open the back wall to reveal a pair of medikits.
There is a S-shaped tunnel to the north-west from circular lava-filled room. After second turn, you can see a "vent" near the floor on the wall to your left. (Similar "vents" are commonly used in maps for setting off monsters by means of propagating player's gunshot sounds.) This "vent" is actually a fake wall, behind which lies the passage to a hidden room. After killing everyone in there, flip the switch and step into the teleporter to be taken to the tunnel where you came from.
In the courtyard with tower in center, columns along the perimeter are placed in a pattern, alternating between stone and metallic. Metallic ones can be lowered to reveal some goodies. Look for the column that breaks the pattern (in the southwest corner), which contains a megasphere.