Mistress Cogita says to visit Firespit Island to find a pokémon who may have a Plate for you.
Go to the Cobalt Coastlands
After you have talked to Mistress Cogita about Firespit Island, during The Researcher of Myths, go to the Cobalt Coastlands, and Palina and Irida will meet you when you arrive.
Go to Firespit Island
Go to Molten Arena and find Iscan and Irida near where you fought the Noble Arcanine. Approach them, then enter the cave.
Catch Heatran
Avoid Heatran's attacks. You will need to move quickly to do so. Throw balls of mud at Heatran until its flame barrier is down (there are balls of mud scattered around the floor if you need them), then when Heatran is stunned, throw a pokémon at it to start the battle. Reduce its HP and inflict status ailments to improve your chances of capturing it, then throw Ultra Balls (or whatever types of Poké Balls you have available) until you catch it.
Afterward, you get the Iron Plate.