One thing I noticed is that the TGT drops to a temperature close to ambient almost immediately after shutdown.

Temperature should drop much slower (should take 1-2hrs to drop back to ambient temp). And if you wanna go the extra mile there should be a little bump of temperature caused by heat soak a few minutes after shutting down engine:

(note: the curve below is a generic dual spool axial gas turbine, not a tay-specific one)

Thanks guys