That's the "how to"... Use a contactor controlled by the Smart outlet... the contactor needs to be rated at about 120% of the current demand for safety and to meet any electrical code. You could also set it up with an SSR... SSR is a Solid State Relay, that does the same thing the contactor does, except completely silent. They're easier to use in my opinion, but a lot of folks stick to the old school contactor (which is just a heavy duty relay)... due to familiarity. If using the SSR, I always go double the rating for durability... If I need 20 amps I buy 40, etc...You will likely need a Heat sink on the SSR as well, so plan and research the parts and what they do... It's pretty easy.
I do a lot of electrical stuff for my powder coating oven arrangements... and find that I get better service out of the SSR than the contactor over time.