Micky wrote, on Mon, 30 Nov 2015 18:32:49 -0500:

I don't think a good connection would generate any noticeable heat
even if it was putting out twice the proper amperage.

This is a good point. So, I'm assuming the cable is bad and I switched
cables and at the moment, there is no heat.

As for the 40Watt figure, I think it's a lie because I googled
for the part number that is printed on the side of the unit:
https://i.imgur.com/8bl7ypU.jpg

Notice that HC363-5U printed on the unit?

Googling for just that, I find the same unit only with a different
set of markings, which is listed as being 35Watts, which is closer
to the 34 Watts that 6.8 Amps gets us at 5 VDC:
http://www.amazon.com/Hausbell-35W-H.../dp/B00NUREFMO
"Hausbell 35W HC363-5U UL Certified (UL No:E310745)
Family-Sized USB Wall Charger Plug Smart Charger,
Single USB Output 2.4A Max,Output total 6.8A Max,5P-USB Output
for Apple and Android Smartphones,Tablets and More(White)
by Hausbell, Price: $59.99 & FREE Shipping"

Here's the same unit, this time for $15 but it also calls it 35 Watts:
http://www.amazon.com/Hausbell-Charg.../dp/B00ORLR1X2

Here's another, again listing it as 35Watts:
http://www.sportinggoodsoutdoor.com/...Apple-and.html

And another listing it as 35 Watts:
http://hausbell.net/products/cell-ph...utput-238.html

And another listing it as 35Watts:
http://macbookpro.deal2hand.com/revi...00ORLR1X2.html

So, pretty much, the 40Watts is either a bold-faced lie, or it's
not the wattage of the output (which is closer to 34 Watts).