The Hothouse can only be grown at a special plant pot outside providing you've bought a Cactus Essence from Niccolo.
This is a cactus shaped tardis. Inside it are 3 rooms - the lobby with a friendly cactus called Li'l Cactus, a handyman, and an orchard with a giant talking tree called Trent.
Later on in the game Watts the blacksmith will move into your handyman and will offer to forge and temper armor and weapons, but you'll need the materials with you for him to do it.
Trent will grow fruit and vegetables for you if you feed him 2 seeds. After a few days the produce will grow in his branches and you can climb up the wooden lattice and harvest it. Fruit is very useful for tempering equipment and physicians in some towns can also make elixirs out of a special fruit and vegetable combination.
If you speak to Li'l Cactus he'll get up and write on his notepad of your latest adventure when you leave the Hothouse. While it's not entirely possible for him to note down every adventure you've taken part in (some happen earlier in the game before you get the essence) he can write some quirky comments about them.