In order to be able to complete the Boiler Room puzzle you need to have completed Cassandra’s Medicine Bottle Puzzle first to get the Broken Plate piece from her room and the Cellar key from the Drawing Room.
Then head into the Wine Cellar, get the switch off the shelf to the left of the circuit box, add it to the circuit box and blow the power. Grab the valve off the tank and use the it on the Boiler in order to stop the steam. Then you can get the second broken plate piece which is in the little room past the boiler.
This picture can also be found in Jeremy’s Commonplace book.
Once the picture is complete, you can look at the front of the boiler to find the Talisman numbers. 9 is on the largest dial, 7 is on the middle sized dial, 5 is on the smallest dial. When inputting those into the Talisman, that means 9 is in the outer, 7 is in the middle and 5 is in the inner.
You can then input these into the Talisman to complete the puzzle.