I noticed you said your CHE is centered -- might want to keep that on the warm side so she has an adequate cool side. How old is she? The log hides often don't provide enough security since both ends are open, even with moss.
What are your temperatures at on each side + ambient and what is the humidity at? I wouldn't worry too much about her falling from her climbing stick -- this happens and they learn just like human kids. I would definitely opt for a thermostat so you can help control the environment as vivi said and an IR temp gun (I bought the same one as KMG when I started and I still use it).
Don't worry, you're going to do great. The important thing is that you care enough to make it right!