This is OT, but what case is this?
Also slightly OT, but
don't operate a NEX in a half-case like this!
I'm sure you know that most digital cameras generate a lot of heat -- e.g., a NEX in video capture with an EyeFi card in it gets very warm. Unless it is very cold out and you want to keep the battery warm, you want that heat to dissipate as fast as possible. Most semiconductor components degrade much more quickly when operated at higher temperatures, so you could be dramatically increasing the probability of developing
permanent sensor pixel defects, etc. -- not just getting shorter video record times.
In fact, the LCD itself traps enough heat so that pulling it out a bit from the camera back noticeably improves video time-to-overheat on both my NEX-5 and A55.