does each machine have a dedicated charger or do they just plug in to first empty slot
if using any charger one bad plug can spread through the fleet very quickly. ie one charger plug partially melted will damage that battery which will damage that fork, next night that battery damages another charger whilst the original faulty charger starts on a new fork
do all the operators use the pull handle to seat the plugs correctly
is there a build up of dirt inside the forklift plug connector stopping the plug from going all the way in.
and as others have said correctly installing terminals on to cable is very important

If the connectors have no issue during chargeing it would lead me to believe that the issue is with the terminal crimps on the machine cables if the heat build up concentrated only in the area of the connector (an infrared heat gun would reveal this, your hand works too) run the machine hard ,check the temp along the entire length of the cable, if the entire cable(machine side) gets hot its too small for the current load. If only the area around the connector gets warm I would SOLDIER on new terminals( are these also being replaced after an incident? or is the plastic houseing only replaced )how big are your connectors? Are they possibly under sized?

What condition are the batteries in are they maintained good and have distilled water added to them or are they neglected and always running with the cells dry, how old are the batteries?

yes edward your probably right, cable sizing has always been confusing to me at times depending on what type of cable it is so my post may have been totally incorrect
sorry if it was misleading

My opinion is that the connectors are causing the problem. If you don't have the proper tool to crimp the contacts on then you should solder them on. Make sure they are clean and use a new plastic housing.

swoop, #4 cables would be small but when you get into the */0 (ought) the cable diameter increases the larger the first number, so 4 /0 would be rather large, like for a fast charger, normally a battery would have 1/0 or 2/0, with 2/0 being the larger of those 2 cable sizes.
I would normally say this is most likely caused by the cable charger half laying on the floor and getting run over, causing the lack of spring pressure because the plastic part that hold pressure is weakened (but not all the way broken)and when it gets hot during charging, it then weakens the same part in the truck half. spreading the problem further.

usually if the connectors between the truck and battery melting tells me it is either just bad connections due to loose spring tabs in the connectors, not holding the contacts in the connector together tight enough. Or the terminals are not crimped correctly.

the part about the cables on the battery tho makes me suspicious, 4/0 cables are a bit small
what voltage is the truck? i'll assume 36/48?
it could be the batteries were mis-spec'd and have the wrong size cable.

Also could be the truck is not setup correctly, high amp draw from incorrect motor settings maybe?

one thing is you can get a clamp on amp meter and monitor the trucks amp draw while operating it and see if it is running high. There is also another device you can use called a 'power prover' that hooks up between the battery and truck and monitors the power usage, most reputable dealers have one or your local battery service company should.