Can you clarify cold start roughness?

The cold start valve ("Injector") dumps a ton of fuel in until the thermo-time switch turns it off. A test you could do I suppose is unplug that valve during the roughness and see if it smooths out or not. It could just stall out, of course, but only one way to know.

If your system is on the edge of being too rich the CSV might be dumping too much in, or if your system is on the edge of too lean and the CSV is not dumping enough in due to being plugged or faulty it could also be the cause.

That being said, the thermo-time switch has (as the name would indicate) a designated time it is supposed to be on for, and then turn off. If the thermo-time switch is faulty it could be causing an issue. One way it could be faulty is it turns off too quickly, the other way is that it does not turn on at all, or it stays on too long. These are all things you would need to measure accordingly based on the temperature it reads from the coolant it's in, the 12v heating applied to it to cause it to turn off, and the open or closed signal it sends in response.