Appropriate viv for an adult rat snake?

I am considering adopting a rat snake (black or leucy), and whether I adopt one as a juvenile or adult, I'm thinking ahead to the viv setup. My corn snake is currently in an Exo Terra 36" x 18" x 18" with UTH, which is great because this species is fairly terrestrial. I have noticed, however, that our local nature center's three black rat snakes are quite arboreal, and spend most of their time curled up on the branches high up in their vertical viv rather than in hides on the ground.

I was wondering if an Exo Terra Natural Terrarium Large: Tall or Extra Tall (dimensions 36" x 18" x 24" or 36” x 18” x 36," respectively) with several tiered climbing branches, canopies, and hides, would give an adult rat enough horizontal space?

Also -- if using an UTH for temperature gradient, because of the added height, would I be advised to also use a heat lamp source closer to the top of the viv?

Thank you.