What comes up, must come down, then go out, then go up.
Veni, vidi, vici -- chronologically. (See Gordian's notebook.)
If heat makes things bigger, then cold . . .
Go with the flow of hot to not so hot.
Temple of Caesar/Baths (a.d. IV Id. Iul.)
You'll read about the flooding of the Temple of Caesar due to a malfunction at the nearby Baths. Go to the temple (at the east end of the Forum) and insert the stone key into the altar in front. Pull it right, then left, revealing an unlit torch. Light the torch at the flaming torch to the altar's left. You'll be transported inside. Go down to the pot and release all the water by pulling on the handle at the bottom. When the pot rises, go up, turn so you're facing the pot, and look up quickly. Attach the rope ring to the pot ring, which sends you out of the temple, but opens the main temple doors. Go up to the main doors and enter. At the map, press Gallia, Aegyptus, Asia, Africa (the clue is in Gordian's notebook entry on Julius Caesar -- the order of his campaigns.)
Go through the gate at the right of the map. You'll find yourself on the other side of the room with the pot. Go through the tunnel and enter the barrel-shaped door. Pick up the bar in the sunken area and bring it to the Frigidarium; dip it in the water to cool it down and shrink it. Go to the pump room and attach the bar to the pump by placing the center over the brass knob between the pumps. On the left (marked "Intro") press "C"; on the right ("Exitus") press "T", which drains water from the Calidarium into the "Tepidarium" (i.e., the sunken area you saw before). When the Tepidarium is full, enter the Calidarium and look into the tub -- it should be empty except for a gold box. Open the box and get the curved wire, wooden horse, and scroll. (The clue to all this is in the scrolls -- complaints about the temperature of the baths.) Examine the scroll carefully and play with the animation; you can't take it with you and you can't re-open that gold box once you leave the room. Note that turning the animated valve clockwise shuts the flow of water off; counterclockwise turns it on. This is relevant to one of the possible endings.