It depends on the distance the bulb is from the wood. I'm a Texas Certified fireman. An incandescent light bulb emits heat, even the small ones. A normal 60 watt lightbulb, in a ceramic socket, located on a wooden wall, left burning, will ignite that wooden wall. It may take time, but it eventually will ignite. That is from the results of a fire investigation into a Church fire that I helped fight.
Now, having said that, I'll say this. The low heat from a 7w bulb is still enough to eventually dry the wood to the point that it will combust easier... (it might take a while for the wood to release the gasses that burn)... than it normally would. That's why I said above, that it depends on the distance between the bulb and the wood.
Do you have air holes in the bottom, to allow cooler air in, so the heated air will escape through the holes in the top? If not, I would design some into the piece. It needs air flow in order for the heat to move out.
Do you have a shroud of aluminum around the inside of the wood, which allows air to pass between the aluminum and the wood? If not, that would be another necessary feature. The airflow between the aluminum and the wood will dissipate the heat.
Sorry, this is so long... it's the only way I knew to get the point across. A house fire is an awful thing to experience.
I like the little night light, but it looks too small to have enough space between the bulb and the wood. JMHO Guess I've been a fireman too long.
BTW, it is a nice looking piece. 🙂