If the problem goes away with temperature and low RPMs, this sounds like an issue with the cold-start inputs. Could be the IAC (Carter Motor), TPS (Throttle position sensor) or associated inputs for the cold idle maps (Coolant temp sensor, and in some cases IAT sensor). The IAC is effectively adjusting throttle position on cold temperatures, and the cold-start maps should be providing initial fuel for engine turnover as well as the coolant temperature enrichment maps (the car gets a lot more fuel on startup, and then fueling enrichment tapers off as the car warms). Any idea on battery strength too? I had a few cars with standalone ECU's that would do all sorts of strange things when Voltage was low. I retuned the car 15 times, before simply upsizing the battery and solving the issue.
If you have an OBD2 reader and can reach IAT, Coolant temps, and TPS make sure they're accurately true positions. For TPS maps too, be aware it may rad 0-5% of so, and most ECU's consider some small variance for "idle maps".