Jeff hi,
First, don't panic! I had my moment of panic in August 2012 when I got back home with a brand-new leased Leaf, and found out the 25-foot trickle cable is literally a foot or two too short for comfort... and then like you and everyone else, read the ominous warnings in the vehicle book about never ever using an ext. cord.
I called the dealership when I got it, and they said, as long as you use a thick enough extension cord, and a proper outlet, don't worry about it.
And indeed, for 2 years this has been our sole home charging "terminal": a 25-foot 12-gauge outdoor ext. cord, of the type you get at any hardware store, connecting a grounded 15-amp outlet on our front porch to the Leaf's EVSE. on rainy nights we place the connection on something (say a frisbee or a planting-pot base) and cover it with a circular kids' snow sled, just in case.
We passed all battery checks with flying colors. We never needed to install an L2, because our typical daily driving was not even 20 miles (it's a less-than-commute car, b/c we commute by transit and walking).
Mind you, our porch outlet was installed at least some 30+ years ago. It's up to snuff but not brand-new by any means. The charging current never goes near 15 amps, so if it's rated 15 you should be good to go. An overheating outlet, as some commenter wrote, indicates an under-rated outlet (some are rated only 10A), a worn-out outlet, or poor electrical work.
We did bust one extension cord after about a year. Its plug just physically broke - which reflects very well on how hardy the Leaf's L1 EVSE is.
Now we have a 2014 Leaf, whose EVSE looks even better. Per my reading, the designation "emergency only" has been removed from the Leaf driver book's description of the L1. I think they realized so many people do it on a regular basis.
We did buy a Clipper Creek HCS-40 now (up to 7.2kW), which can connect to my wife's kiln in the garage, on a 50-amp NEMA 6-50 outlet. But we did it because the 2014 has the ability to use 6.6kW, and only as an emergency backup if we need to charge in a hurry and don't want to go sit somewhere and charge - our garage location is extremely inconvenient for nightly parking, and its interior is all taken up by her studio anyway. Objectively it's probably a poor investment ($665), but I thought it'd be nice to support Clipper Creek and have this back-up charging method that might come in handy on some road trips with the right adapters.
Anyway, get that 12-gauge cord, and don't spend extra money before you know you really need to! That's my 2 cents at least
Oh, and congratulations on your Leaf!
Assaf