A hatchling BP can easily touch the top when the tub is only 7" high. I can't speak for what others do, but I've only ever used a tub that height for brumating snakes in winter. (ie. with NO heat whatsoever). Honestly, taller would be safer, IMO.
Also- what kind of t-stat is controlling the CHE? If it's the "on-off" type, it's going to be on full blast at times, making the heat a risk whenever it's "on". Hopefully it's the proportional type, that continuously dims the output, if (?) a CHE will function that way. (I don't use CHE, so I'm not sure.)