If the Temple of Hermes gets hit and downgraded to Level 1, a player can rebuild it in 2 ways.
The first way is by slowly rebuilding it for free up to Level 6, and then rebuilding it up to Level 9 with Upgrade Sketches. Unfortunately, rebuilding and upgrading the Temple of Hermes this way takes some time, like the common construction of other Buildings.
On the other hand, it is possible to rebuild your Temple of Hermes up to Level 9 instantly by spending Drachmas. Sketches are also required each time the Temple of Hermes is upgraded to Level 7 and higher.