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Ha, mine started doing the same thing. Before it was stalling when I pushed the clutch in/dropped it to neutral (at any engine temp). Now I replaced the IAC and now it has trouble starting cold and staying running, but runs great when warmed. Following this thread to see what solutions you may find.
edit: I did not try warming only the ECU and then cold starting the engine. I'll give it a try.
If possible I'd dismantle the ECU and check the soldered connections inside, check for charred, burnt or odd looking solder joints and get out the soldering iron and redo them.
I have another car where that's a common problem in the cluster.