I did almost the exact same thing with a cheap plug-in sconce from a big box store. Mine got warm at the plug end, not the cord, and I traced it back to a loose outlet that was half dead. Old power strips are the worst for this, they were never meant to carry a space heater plus anything else. You probably didn't get a bad light at all, you just stacked too much on one strip. Try the sconce alone in a wall outlet for an hour and see if it still warms up, my guess is it stays cool.

Is it just me or does this happen with a lot of stuff we buy now? We get sold the "better" version of everything, more features, longer, fancier, and half the time the plain old thing your parents used did the job fine. I've noticed it with kitchen stuff too, my mom's cheap old pan beats the expensive nonstick one I got. Maybe the retractable leash is fine for some dogs but it seems like a lot of people end up back at the simple one. Your dad probably didn't explain because to him it was just common sense.