450 watts @ 12 V is 37.5 amps. That's way too much for a single run of 12g cable. Split your lights between two runs of the cable. I'd place no more than 300 watts on each cable. Less if the distances are very long.

The other issue with splices melting is usually because they weren't done well to begin with which causes a excess resistance (equals heat, especially with large currents going through them).

Ron, I only have 250 on one run and 200 on the other, 450 total going to the Transistor but split up on 2 seperate runs.

You shouldn't use regular wire nuts outdoors no matter how great you think things are sealed up. Use the proper outdoor rated connections.

So thats the only obvious issue you see correct? I should be able to cut back the wires, resplice w waterproof nuts w silicone and the problem should be solved? Just corosion on the wires/moisture in hub could be causing the melting occasionally?

Usually when I have seen connections involving melting or welding together, it has been due to arcing, which means the connection is not tight in the first place. Make sure they are done well. There are various opinions on how to do wire nuts (either to pretwist or let the nut twist it), but I prefer to pretwist and ensure they are together tight before the nut, then put the nut on for good measure. Pretwist in the correct direction, and the nut will make it tighter when you put it on. If you pretwist it the wrong way the nut will untwist it when you put it on. Linesman pliers is what is used for twisting.

I will support the dissenting view. You should follow the manufacturers instructions. Pretwisting does little in the long run for wirenuts other than hold things in place while you get the nut on. At worst, they give you a false sense of security.

Waterproof connectors are not just a good idea, they are ESSENTIAL. Anything underground (no matter how great you think you've sealed it) is by definition an WET location.

Thank you both for the input. Again, im not sure that it matters (i was told that there is a difference), these connections are NOT being done underground, they are being done in an above ground sealed HUB. I just could never seem to feel like I am getting a nice tight connection when using the silicone nuts when connecting 3 wires.

If it is not staying tight, pretwist is your friend. And you might be using the wrong size nut. I disagree with ron on the pretwisting (again everyone has their own opinion on this). I have taken off various nuts not pretwisted and the wires are completely loose, or they arced so much that they were welded together and I couldn't get the nut off. When I take off a nut on my pretwisted connections they are still together tight. So the claim that pretwisting does little in the long run is wrong. I have read an entire thread on a different forum of people going back and forth on this so whatever works for you. I personally have had to redo a lot of junction boxes with loose connections done by someone else and have never had a problem with my connections. The connections of mine that I have undone were for later modifications and they were just as tight as ever after taking the nut off.

One of the valid arguments against pretwisting is that when that is all you do all day it is extra wear on your wrist, which I agree with. If the nut alone could twist the wire and get it tight and keep it tight then I wouldn't pretwist, but I have not experienced that in the limited electrical work I have done.

Outside wiring is cordage and has different ampacity than interior cabling.

So my best option would probably be to swap out wire and use 10/2 since it will carry more of a load (288 watts at 80%) correct? That way I could still break up my 9 lights how I currently have them, with 5 being on one run (250 watts) and 4 being on the other (200 watts). Changing out the wire and then making sure the splices are solid at the hub should probably keep these issues from occurring. Is this accurate?

If I broke up my 9 lights into 3 runs (of 3 lights/150 watts on each run), I would run into another issue of overloading my transformers since its a 600 watt, which has (2) 300 watt connections therefore I would have to put 2 runs on one and 1 run on the other, therefore overloading and maxing one side of the transformer.

Why does the house direction matter? Just curious. 12/2 cable, not sure rating, was standard cable from Lowes, the 2 runs from transformer to hub are approx 15-18' (hub is shown in diagram), 12 volt, 50w halogen floods, all the same, house faces north, wire only buried below 2-3 inches of mulch in most places.

The front of my house does not get all the afternoon sun, and I live in Chicago so the ground temp is not at 120F. Dont assume everyone on here is a complete idiot. I used 25 watt when initially installing the lights and it was not even close to as bright as the 50, thats why we went with what we did. Im not having any issue with voltage drop or anything else. The solution that would make the most sense would be the splicing. Ill fix that first and see how things react. Rarely have problems to that degree. Thanks for the responses.

Are those two sets of terminals connected together at the transformer? If not, then the transformer box may in actuality have two 300 watt transformers in it and you could not do what you propose.

They are not, basically 2 300 watts as you stated. Any suggestions then? Keep as is but use 10 gauge instead since I can put more wattage on the runs with 10 gauge?

I realize your problem was 4 years ago -- we have searched on line for our problem and yours came up. Our connector is melting (looks burned) always at the same place. When we separate the 12 gage wire to cut and replace the gel filled connector, one of separated wires is no longer brass looking, it is black looking. Have not been able to find anything about wires going bad. Our wattage on the transformer is fine. Unfortunately, the wire goes under the sidewalk to supply the other lights so we are a little stuck. Did you find your cause for melting.

Wheeler does your lights turn on at all after you redo the splice or does it immediately trip breaker?

https://www.amazon.com/stores/King+Innovation/page/A8E7536E-7951-4DD4-866D-707C150932EE?ref_=ast_bln use these they will give you the best connection but suggest use a crimp and not just pliers