M10 4 cylinder engine swap

[Bimmerman85]

Hi everyone. My son has a 1985 E30 coupe with an M10 and manual transmission. There are issues with the M10, mostly related to idle problems, and I was wondering if there is another BMW 4 cylinder engine that can be swapped into the car that will bolt up to the stock 5 speed manual transmission? Or even better, is there a way to replace the stock jetronic system with a newer BMW or aftermarket system to control ignition and fuel systems. The car has major issues in the cold weather with surging idle, and a mechanic friend of mine told me that he thinks the idle stabilization relay is the cause of the problem, but we can't find a new or used one around here anywhere. Second, in warm weather the car idles poorly when warming up after a cold start, and sometimes stalls. If you start it up and then drive it right away, the engine will idle better after you drive for a minute or so. I suspected a faulty cold start valve, but haven't found it leaking and have even tried leaving it in the manifold with the electrical and fuel disconnected from it without any change. I am not sure whether to try and swap the engine or update / upgrade the engine management system to something a bit newer like a Motronic system. Any suggestions?