1995 Mazda Protege Cold start problem

Dear Sir,
I have a 95 Mazda Protege with the twin cam 1.8 engine. Only when the engine is stone cold this problem exists.

I crank to start and it catches for half a second, then it wants to die, then before it stops spinning it catches again, goes up to high idle and runs fine.

Hot starts no problem, or even when it sits for 4 to 5 hours no problem. It will start fine and go up to high idle, come back down and run fine. Only when it sits overnight it will do this. The colder it is, the worse it does it. Never had to re start it, but it may get worse.