I think my husband first came up with the terms "thinking brain" and "feeling brain" about two months ago. My immediate response was unease as this seemed to establish the idea of a mind-body dichotomy (http://aynrandlexicon.com/lexicon/soul-body_dichotomy.html). Cameron has absolutely latched on to the terms and really likes talking about his thinking brain and sighting examples of when he's used it well. For example, he recently got sealants on his teeth and was absolutely crowing about how strong his thinking brain had been because he knew it hurt a bit but was better for him in the long run. I love seeing that pride in his accomplishments. He also seems to love the idea of exercising his thinking brain, making it stronger, helping him become an airplane engineer (latest passion, he's moved on from wanting to be a circus acrobat)!
So, we've done lots of talking about how both "brains" are important and all the wonderful things that feelings offer. He is so intensely joyful and has no difficulty grasping that feelings are good too. He also understands, at some level, that feelings are not thinking i.e. they just happen and need to be evaluated before action. While we're working with these terms, I'm curious what language other Objectivist parents have used. If exercising their brain, making thinking stronger, or somehow pinpointing the cognitive issue has come up for other parents, I'd love to hear how you've handled the issue in the comments.