There are a few heavy-duty options which will typically support up to 40 A, but they are quite large and industrial looking, so I don’t know if that meets your requirements. They work well for things like pool pumps or water heaters, but would look pretty strange for a bedroom air conditioner.
See the following thread:
There is also a 20 amp zwave fixture relay Which works well if you have room to install it. It’s made by Nortek and is sold under multiple different brand names including Linear and Nutone.