in my experience with electrical connections...and I have 16 years experience...the only time that a connection burns up is from a bad or loose connection. There are some instances where the current through the connection is too high which can cause discoloration or burning, but usually the weakest link is the first to go. So...if your terminals are burning, find a way to make the connection better, maybe solder it, then if the amperage is too high, something else will give...eventually.
That could work, but you would have to make sure where your wire comes out of the box is sealed up. If you look at Troy Jones original post of the 4 18" btl w/ 4 mojo 4kw. One of the photos shows that he uses a machine screw or something of the sort to connect the wires to inside the box, and I'm sure the same thing on the outside of the box also. That way the box is still air tight (except for the port) and you have a good connection. I would post the picture but the site is doing something funky and your thread is the only thing coming up.
1. Use bigger wires both inside and outside the box. 2. Make sure the connection is solid, not loose wire twised around a terminal.
If you still have problems after that you trying to use cheap terminals that cant handle as much power as your trying to push through them, but then again not many terminals can handle the power that alot of people push to there systems now days..... so they use bolts and butterfly nuts :p
I'd make sure you're using at least a good 12 guage wire if you aren't already, and like glove said check your connections. As far as the terminals I used- just 3" althread. 3/8 threaded rod, drilled out a hole 5/16 of an inch and screwed the rod in. It forms a nice air tight terminal, then tighten the wire in place from either side using a terminal crimped on to the wire and a nut (some washers help too).
I was looking at some things at lowes- go to the electrical section where they keep the breaker stuff, there's things that will also work there that only need one screw and an allen key. ;)
If your wires kkp burning up at the terminals, Then I would be hesitant about running it direct. It may toast the amp terminals, or worse, the subs terminals. Replace that wire with some quality 10-12 awg. Check your amps ground. Terminals should not be getting fried, unless your putting some stupid power through them. What amp and sub combo you running? The threaded rod thing is a good idea, but I would try to find out why they are heating up in the first place. Thats not normal...