Paul,
In a fully ducted (bypassed) installation, it is a good idea to allow cooling airflow to exit the nozzle area by using an augmenter at the nozzle. Take a look at a BVM Bandit some time, and you will notice a gap around the nozzle that allows air to be sucked from the aft fuselage by the exhaust gas velocity. The tailpipe is actually positioned about .700 in front of the augmentor sleeve aft edge, creating suction in the aft fuselage to carry heated cooling air out of the fuselage.

The top of the aft fuselage will always get hotter than the bottom, so you can make a lightweight insulation blanket out of BVM ceramic heat blanket material (Fiberfrax) and cover it with aluminum foil. Make a template out of paper to fit the fuselage shape, cut the ceramic to size with scissors, glue the aluminum foil to it, and glue it to the upper fuselage inner skin with dots of high temp silicone adhesive, foil side out. High temp silicone is made by Permatex (and others), and is red in color, and works extremely well for this job.
With the turbine running, you will not feel any more heat from the pipe.

BVM "Heat Shield" is a water based silica compound (paint brushable) that will insulate any surface that you apply it to. Use three coats, with drying time between, and the surface will be protected from direct flames long enough for you to blast it with CO2.

IMHO, you should still allow the heated air to exit the fuselage, lest it becomes an oven.

Static thrust isn't all we are looking for....Dynamic thrust is what flies the airplane.
Measuring the static thrust isn't a total indicator of which combination will go the fastest.....The airframe flies in a dynamic environment..... Aero, thrust, total drag count.

harley Condra
BVM REP
JetCat REP