No, it does not!
I know nothing about wall furnaces, I’ve never seen one. But I do know one thing, you cannot mix combustion gas with indoor air!
There are two vents on a wall furnace, one for air to come into the furnace and one to discharge it from the furnace after it’s been heated.
The combustion air vent is located behind this internal duct, which goes from the furnace air intake to the roof. This is not like big furnaces that have barometric dampers to add air to the flu draft, which may be confusing you.
Excessive heat in the indoor air circuit is generally related to an adequate airflow, allowing excessive temperatures to occur within the system.
If you are in the winter season you could run the unit and get a temperature rise through the unit with a thermometer, which would give us something to work with.
Best thing is to just have someone check it because the blistering paint is not a normal occurrence. It’s not your job to analyze, but it is to know how the systems work, so you can test them.
Never ever is combustion air allowed to connect with the indoor air.