I was thinking this is a vacuum problem, that goes away when sufficient heat builds. I am searching for a common problem that causes that symptom.

What does it do when it is cold? It probably dies and has a low idle and rouns rough. A fuel pressure check would be the first place to start. If the ignition system is in order. Since CIS fuel injection depends on pressure differentials to make the car run well, a qualified tech should check for injector leakdown, and cold fuel pressure. If I had to guess you might have a stuck warm up regulater. They can be adjusted be a qualified person.