It's more likely to be a duff iscv, if the reading is correct at one point it is 99% likely correct at all temp points.
Once the engine is warm check the CO is what stu says for that chip, normally around 2.5%, you could always tweak it up a touch, as it sounds like it may just be a bit lean.
It's very hard to get the cold stuff 100% right for every car with an off the shelf chip, as there is always variations.
In short it is a chip not a live map, if it was mapped individually then you would not need throttle, so long as iscv working ok, have a look also for any air leaks as these will lean the mix, you could also tweak the tps reading a touch so it gets slightly more fuel.
Cars can start perfectly stone cold with no throttle and with no iscv if set up correctly on a decent ecu.
tabetha