Sending 120VAC to a device for a certain amount of time after a single button press
You can buy buttons that do exactly that. They are often pneumatic, holding themselves in until enough air has leaked in to release them. They're used for lighting stair wells, etc.

Alternatively a 555 timer in monostable mode driving a relay, or a small microcontroller doing the same job (easier to make configurable and get more precise times).