The module controls ignition. Rough running isn't usually how it manifests - usually if the module is starting to fail under heat it will kill the engine, then allow it to be started after it has cooled off for a few minutes. "Running like" crap isn't very helpful, but since it's running at all, I'd suggest the module is not the most likely candidate. If you want to test it, have a thermos of ice water handy and when the engine starts to run poorly, pour it on the module (small squarish box, front side of distributor). If it immediately runs better, the module is the problem. (Based on symptoms, not the most likely cause.)
I'm starting to wonder if there's a temp sensor sending bad info to the ECU. I haven't had to diagnose such a problem, but perhaps someone else can help. I suppose one thing you can do is disconnect the temp sensor(s) and see if the engine runs differently than it is now.