If a volume of air enclosed by a physical box is kept at a constant temperature that's different from the temperature outside, will the temperature of the inner wall of the box be the same as the temperature of the air?
Heat will always travel from the hot place to the colder region. So if the air outside is colder than the air inside the box, even insulated walls will let the heat travel outwards and lower the temperature of the box.
You will have to keep supplying heat into the box if you want to keep the air and wall temperature constant.
There is no such thing as 100 per cent perfect insulation so the air inside the box and the inner wall will eventually get to the same temperature as the outside air. This is reversed if the outside air is hotter than the inside air. The heat will flow into the box.
The main point to remember is that to keep the temperature constant in the box and inner wall, you need to keep heating it if the air outside is colder. Or keep cooling it if the air outside is hotter
If you Google "second law of thermodynamics" you will find out more about this process and also learn about entropy, which is related to it.
It's a good question to ask and I hope this helps to answer it.