GT stutters and hesitates on low rpm when engine is hot

Hello,
I'm new to the forum and i have a shipped GT 2005 Automatic from USA to Lebanon.
The car is stock not modded.
The engines runs smooth and in full power when its cool but after driving around 30 minutes or after sitting in a traffic and the engine gets hotter the car starts to stutter and hesitate on low rpm between 1000-3000 and i can feel the power cutting down.
A WOT also stutter before 3000rpm
Performance on high way is noticed to be down.

This only occurs when the engine gets hot.
When it is cold the car is aggressive and runs in full power.

The temp gauge needle is in the middle.
The fan opens normally.
Water and coolant are in normal level.
A scanner showed no problems at all.

Any help is appreciated
Thank you

streethorse said:

How many miles on the spark plugs? That would be the first thing to rule out.

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The car is shipped for usa to my country so im not sure how many miles the spark plugs ran on it.
Does a spark plug do this problem only on low rpm? why its not continuous and why not when the engine is cold?

streethorse said:

Well, how many miles are on the car itself ??? If it has around 100k miles
and still has the original plugs they definatly need changing.
Many problems are exagerated or more noticable when the engine is hot.

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Yes it has 114k, is it possible the old owner didnt change them!
Ill replace them and see what comes.
But the problem we dont't have Motorcraft no Brisk nor Autolite in here, only NGK and Champion, shall i go -1 heat range or stay on the stock one.