The cable connecting to the positive terminal on my 2000w inverter is melting.

You need a bigger power line the longer the run the larger the wire
Also look for loose connections at that power stud and you need a properly sized circuit breaker or fuse close to the battery source.

 

He’ll just looking at the picture the lug on the end of the power cable looks to be the wrong size also. But I would definitely upgrade the power wires use a high strand tin covered battery cable anchor is one of my go to for battery cables and you can buy a great hydraulic crimping tool from Harbor freight.

 

The connection and wire looks corroded. Corrosion causes high resistance which causes heat and why the cable melted. If you were ok for 6 months with the 750 watt burner only replacing the cable should be enough. I don't see any reason to drop to a 500 watt burner.

 

Looking at it another way, corrosion causing resistance isn't the start of the problem, heat causes melting which causes corrosion which causes resistance. It all starts with heat melting things (from improperly sized wires/connectors) or a loose connection, both of which cause corrosion, which causes fires.

Corrosion CAN cause resistance, of course, such as corrosion on any chassis battery mostly because they are out in the elements, but on an inverter it's usually heat melting something or a loose connection which starts the chain reaction.

Properly sizing cables/lugs for big inverters is probably the #1 thing people screw up in DIY inverter installs. For most people it's hard to fathom the huge cables needed to run inverters to power high load kitchen appliances like microwaves, hot plates and coffee makers. And most skip the fuses and breakers which are the first line of defense that you have a problem. This is just like wiring your house without a breaker box. Not at all a smart idea.

 

https://www.amazon.ca/gp/aw/d/B0D9LRDPDK?psc=1&ref=ppx_pop_mob_b_asin_title&th=1



Under $100 for everything you need to beef up your wiring

 

Yep, that's a great price too if the quality is decent.

 

Looks to me like a poor connection, causing heat. These days when I make cables I solder the ends and crimp them as well. Then cover the joint in heat shrink with the sealer. Rarely have any issues.

Hard to guess the wire size in the picture and length is unknown but your absolute max current draw probably would not exceed about 60 amps with a 750 watt peak inverter. There are charts online indicating max current load for a given wire size and it's length. When in doubt it doesn't hurt to go to the next heavier wire gauge.

 

Just noticed you said burner and not inverter. Disregard what I quoted for the amperage draw. You'll have severely undersized wiring since your inverter is probably bigger than 750 watts.