Electronic Ign. Control Unit (ECU) Heat condition

Ballast resistor? For a Mopar box ballast resistance plus coil resistance is 2 to 3 Ohms. What what coil? What is battery voltage running? All questions relate to ignition primary current, that is what heats ECU.
Guys,
Really appreciate all the feedback. I ALSO strongly believe I am simply not getting sufficient voltage to the started/relay circuits under hot conditions. I will take several voltage and resistance readings as suggested, re-check all ground and + connections points, and see what I have. Will probably replace the ECU as a matter of good practice along the way, though right now the car starts quick(when cold), and runs smooth across the rev range. Probably just replace the ballast resistor as well...(I do have a slight stumble just off idle but I am pretty sure that is Carb issue--came with a Demon 800 cfm --which I think is too big). The + Battery cable from trunk to starter looks new and is 2ga which looks like a pretty "healthy" size (but I have never had a trunk mount before). The 18" ground cable running just under the trunk to a frame mount is also 2Ga. Engine ground consists of an ~16-18" cable (slightly smaller than the 2Ga size) running from front of engine block to a radiator bolt.