I think I figured it out. It's voltage to the ECU. Either a bad power, or a bad ground.
I don't think this would be temperature dependent. True?
\D
Well, everything runs OK on pre-set values. The issue obviously occurs after the ECU starts running things off of the sensors. Since the sensors aren't the issue, the issue is somewhere with the ECU itself. Unless the ECU is bad, the issue is voltage. The ECU does not start running off the sensors until the engine has warmed up, so yes, something with the engine being warm.
Since voltage has a dramatic effect on the ECU, that is a highly likely source of the issue.
In theory, when you unplugged the CTS, resistance should have gone to infinite, as in cold. Unless there is a short somewhere.
Keep in mind that the L4 is foreign to me.