What size are the cables? Are they ALL of the same size? Innter connects large also? I dont invert my heavy loads but do run number 2 on all the battery stuff and number 4 on solar in and out. What size cable to the inverter? How far is the inverter from the battery? I would run 2/0 or 3/0 to that inverter if it's within a few feet of the battery.
If I was inverting to 2000 watts I would also run heavier than number 2 on my batteries.
With the system loaded you can use a digital meter to look for voltage drop of individual conductors. You may be losing more than you like and not generate a lot of heat. Volt meter is going to be more accurate than a temp reading. If you have several poor connection points or under sizing in general you can get a total resistance that will hurt you but not see a lot of heat at any one point.
If you had one very bad connection point such as a loose cable it would show as hot, it may even be too hot to touch, it may even start to smoke and melt.
It's extremely important to have all the wiring sized large enough or you are penalized forever. My solar should basically be ok with 6 gauge but I ran 4. 520 watts with about 3 feet from the solar control to batts and 12 feet from solar control to combiner box.
You dont want any push in type fuse holders in your solar system either. No crimp plier terminal ends, hyd crimped ends and bare strand into terminal strips with set screws not yellow crimp on ends.
