Summarize:

If the cord feels unusually hot to the touch, stop using it and check that the appliances plugged into it do not draw a higher amperage than what the cord is rated to handle. Consider a heavy-duty extension cord meant specifically for large appliances where applicable. Replace or repair loose or frayed cords. Consider having additional circuits or outlets added by a qualified electrician so you do not have to use extension cords. These will shut down if overloaded.
Do not overload extension cords. Regularly check your extension cords to make sure the plastic is not worn away or coming apart at the ends. Avoid using an extension cord as permanent wiring. Instead of a simple extension cord, get a laboratory-tested extension cord with built-in circuit breakers. Avoid running extension cords across doorways or under carpets.