First of all what an interesting question..
I'm assuming you have a clean air filter fist of all .
And your right the stepper acts a cold start firstly then as the engine warms up it closes down so it's not running too lean.
The ECU is supposed to then track the idle speed and adjust the stepper/timing and injectors to give a constant idle.
Or so I've been lead to believe.
I recently had the opposite problem after my stepper control housing fell apart , I had to buy another stepper motor from a triumph 955i. And also put the housing back together with super glue to prevent extra air being drawn in as I couldn't get the idle below 2,200rpm !.. it drove me nuts .
So my thoughts are leading to the map you have installed on the ECU.
it's quite possible that it's extremely Rich on tickover.
I've noticed that you can can adjust adjust the tickover via the screw though.
So why not just reset the TPS when the engine is hot and you've adjusted the tickover to a happy place ? .
Hope this helps .. but I may be totally wrong .