Mine is currently in the shop for a similar fix. Cold starts are fine, but warm starts stutter and stall. The crankshaft and camshaft sensors started throwing codes. I replaced the crankshaft sensor (do not recommend on your own unless you have time, patience, and mutlijointed/skinny arms) but was not in the mood to tear down for the camshaft sensor. I actually stopped by the shop yesterday to talk to my new mechanic about the S/C install so he could get more accustomed to the mods to know what he was tackling. He did some head scratching as the cold vs warm boot is pretty elusive, but he is also confident that replacing the camshaft sensor so it can marry information to and from the crank sensor is the best place to start.
Like etl said though, get those codes read. You will be hunting for a needle in a haystack until you do so.
Gary Noonan
'01 S/C VX / '18 Forester XT