wires underneath the ignition key are seemingly to melt, should I replace them or should I give the HVAC controls their own ground

 

Depends. It shouldn't be necessary if all is in good working condition.
Which wires are melting?
Can you take a picture?

 

You need to address this soon and correctly. do not run the device that causes this until fixed. Often a high resistance connection one that got dirty, corroded, or loose causes heat when current flows, that heat is generated at the poor connection, and travels easily along a copper wire. The heat makes the connection worse as heat aids in corrosion formation, and heat cycles can loosen connection, and cause permanent loss in spring tension of connectors that need that spring tension to maintain good contact.

Likely there is a bad wire crimp or connector that is the root cause. that need be found and fixed. if the spring tension of a connector is gone, then a new spring part is needed, as the spring temper was heated out of it.

the heat will travel the connection will get worse, other wires maybe damaged by heat, the harness can be damaged, depending which wires are in the harness nearby, extensive, expensive damage can occur.

look for areas that got the hottest, that will lead you toward the source of the problem.

 

what year XJ do you have ?

pre 97 XJ have all fan current running thru the ignition switch, a recipe for disaster, I relayed mine out

They fixed this design flaw on 97 and later, which have a common earth/ground system

 

1995 country, sorry about the diagram. all of the HVAC still work. but the red and the Violet wires were melted starting from the ignition wire connector all the way to the steering column. I have replaced wires and also new female connectors into the ignition connector. fingers crossed. I'd be interested in knowing how to replace the wire to the HVAC controls themselves. thanks in advance guys

 

When you say with the AC on, do you mean only with it on AC or with the heater controls on in any position?

The red and violet wires are both involved in powering the blower motor which is likely seized or much stiffer to turn than it should be.