Eventually, your corn will outgrow a 20 gallon, but you'll be fine for a good while. My adult King is in a 40breeder and uses every inch. I'm actually looking into going bigger for him.

And yes, the heat matt is for a hot spot and not ambient temps. So you will need an additional heat source.

Sounds like you're on the right track. Keep researching and studying and you'll be a great keeper