If you found a chest, you will need the key. Three chests are opened as part of the Chapter 1 and Chapter 2 scavenger hunt quests (started with the food scraps and fuzzy dice).
The Hot House quest is referring to the thing in Lukas's workshop near the left wall that looks like it is providing light and heat for the plants to grow. It doesn't highlight as an item to interact with, but put the item to fix it there.