dplavcic

2001 XJ with 143K miles. The engine went on it earlier this year and had a new engine put in back in February. Before then, there were a few times when it was very cold (Michigan winter) that the jeep would only start if you gave it some throttle to maintain rpms. After the new engine was put in, I'm having an issue where it does the same thing except now it happens frequently when it's warmed up. CEL finally came on yesterday and it said cylinder misfire #1-#10. It starts after running errands around town, but will stall out unless I give it some throttle again. It rough idles when you start it cold as well. Could this be the injectors? I've been reading quite a it about the CPS too, but just need some guidance to direct troubleshooting. Acceleration isn't very responsive either. Any help is appreciated!

restoring

I had a similar issue with starting when the engine was already warm, but never had stalling issues. The trouble code was always serious misfire cylinder 3. For me it was the design flaw that literally cooks the #3 fuel injector. After the engine reaches operating temps and is turned off, all that heat from the manifold rises and the #3 injector literally gets the worst of it. This causes a vapor lock type issue inside the injector. When I started the engine back up, it would run exceptionally rough for 30-90 seconds, then smooth out to normal. This could be part of your issue when starting hot.
As for starting cold, I'm not sure. Were new injectors installed with the new engine? Could just be old injectors, clogged, etc.