The EGT is 300-500C and is more than enough to melt the foam. However, it is true that most of the air going thru a turbine is to cool it. The combustion temperature would be above 7000F, if not cooled and the turbine would quickly melt & self destruct.
The air velocity from the turbine exhaust creates low pressure and pulls additional air thru the pipe and fuselage, which keeps everything cool enough for foam.
I find it amazing that such a tiny turbine can be made, and installed in a small foam airplane. If I didn't see it, I wouldn't believe it possible.