Slightly difficult to understand what you're trying to say from lack of periods.
So, what you're saying is the idle is high when you start it but almost dies when warmed up?
So what have you done so far to resolve this issue? Idle Adjustment per vfaq? Logger data? Boost leak test?
If all that checks out ok you may want to look into FIAV blockoff
HERE
I just turned it down as far as it would go and JB Welded it. 3 vehicles now that idle like a dream. Rerouted the coolant hoses as well so they no longer go through the throttle body so there is no chance of coolant leaking into were it shouldn't be.