30 amp power cord overheating

The male plugs have a lot of metal compared to the tabs that rub on them inside the female socket. The breaker may be rated for 30 amps but you'll never get a full 30 amps through it and even if the breaker didn't trip, you'll never get a full 30 amps across the plug/sockets labelled 30 amps. There's just not enough surface area to carry that kind of load. The dielectric grease helps to prevent oxidation which is a killer to a good connection. When using wire nuts, I'll put a little in them, especially if it's in a damp location. I keep a tube in my toolbag so it's handy.

Dielectric grease has really helped my situation. I avoid using the furnace because I can get by with two 1500 watt heaters on their low (800 watt) settings and still use another high draw appliance like the water heater OR the microwave.