Ends of 25' 12/3 and short 14/3 extension cords get warm with 1500W heater
What you're learning is that wire gauge is only part of the equation. As you noted, plugs introduce resistance, and that makes heat. 

You're right that heaters should not be run on extension cords. If you must, use high-grade cords with good plugs, and expect them to get warm. Monitor them for excessive heat which can melt the plastic and cause a failure of the connection. 

FYI, those connections are likely crimped, not soldered.