I don't believe that snakes inherit either temperament or characteristics (such as how they act on a stick).
Snakes change depending on what they're presented with. Also, snakes are built to suit particular things. For example, green tree pythons are thin, light and have extremely prehensile tails. Thus, it is easy to realise they are built for the trees, and are rather unsuitable for the ground. Or that, not unsuitable, just not meant to be on the ground. They are certainly capable to moving on the ground.
Black headeds or womas, on the other hand, are thick and heavy-bodied, and don't have prehensile tails. Same with any of the Antaresia group. Thus, these snakes are not suitable for trees, and it is uncommon to see any of them in trees. In fact, I've never seen a woma up high (except for one, but that was extremely uncomfortable and had to come down quickly), and I've never seen any of the Antaresia in a tree in the wild. I've seen one black-headed in a tree, and that tree was very thick with no relatively thin branches. It was sitting in a burrow and had it's head out in the sun.
Any of the Morelia group have prehensile tails, and thus, can and will be found in trees. They often take the "gtp" position, because that's a very stable way of sitting on a thin branch that they would other wise fall off.
In reference to the other point, how can it be proved that temperament is inherited? Almost all snakes will be snappy when they're young, and will grow out of this stage. It's nature versus nurture. I serial killer isn't born a serial killer. That person would have been brought up in a way that effects them so.
It's the same for snakes. If a snake has been handled roughly and provoked since it was a hatchling, then it will be aggressive. If a snake has been handled gently, and left alone when it wants to be alone, etc, then it will not be aggressive. I've made a post like this before. Everything is instinct based, but snakes react in different ways depending on the situation they have been placed in.
Hope that wasn't too confusing.
~ notechistiger.